Details

Time bar (total: 3.0min)

analyze1.1s (0.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
0%100%0%13
0.1%99.9%0%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample155.0ms (0.1%)

Algorithm
1×intervals
Results
91.0ms63×body2048valid
31.0ms91×body1024valid
11.0ms53×body512valid
6.0ms6×body4096valid
3.0ms22×body256valid
2.0ms21×body128valid
Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify183.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0100514
1100514

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
31.2b
Counts
2 → 1
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

1.8b
(-.f64 x (sin.f64 x))
1.7b
(-.f64 x (tan.f64 x))
0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.7b
(-.f64 x (tan.f64 x))
1.8b
(-.f64 x (sin.f64 x))

rewrite26.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
45×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
25×times-frac_binary64
17×add-cube-cbrt_binary64
14×difference-of-squares_binary64 distribute-lft-out--_binary64
7×add-log-exp_binary64
6×cancel-sign-sub-inv_binary64
5×associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
4×flip3--_binary64 flip--_binary64
3×pow1_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 associate-/r/_binary64
1×cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
3 → 84
Calls

6 calls:

9.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (tan.f64 x))
0.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0ms
(-.f64 x (sin.f64 x))

series215.0ms (0.1%)

Counts
3 → 28
Calls

3 calls:

103.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
70.0ms
(-.f64 x (tan.f64 x))
41.0ms
(-.f64 x (sin.f64 x))
Compiler

Compiled 549 to 391 computations (28.8% saved)

simplify117.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049222250
149222250

prune468.0ms (0.3%)

Pruning

59 alts after pruning (58 fresh and 1 done)

PrunedKeptTotal
New5458112
Fresh000
Picked000
Done011
Total5459113
Error
0b
Counts
113 → 59
Compiler

Compiled 2544 to 1013 computations (60.2% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

1.7b
(-.f64 x (tan.f64 x))
0.0b
(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
0.0b
(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b
(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
1.7b
(-.f64 x (tan.f64 x))
1.8b
(-.f64 x (sin.f64 x))

rewrite40.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
78×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
50×times-frac_binary64
32×log-pow_binary64
31×exp-prod_binary64
30×add-cube-cbrt_binary64
24×difference-of-squares_binary64 distribute-lft-out--_binary64
8×add-log-exp_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64 cancel-sign-sub-inv_binary64
5×associate-/r*_binary64 pow1_binary64 flip3--_binary64 associate-/l*_binary64 flip--_binary64
4×associate-/r/_binary64
3×log-prod_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 div-sub_binary64 div-inv_binary64
1×cbrt-undiv_binary64 rem-log-exp_binary64 exp-diff_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 log-div_binary64
Counts
4 → 128
Calls

8 calls:

11.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
9.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (tan.f64 x))
0.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

series443.0ms (0.2%)

Counts
4 → 40
Calls

4 calls:

241.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
107.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
59.0ms
(-.f64 x (tan.f64 x))
35.0ms
(-.f64 x (sin.f64 x))
Compiler

Compiled 907 to 659 computations (27.3% saved)

simplify59.0ms (0%)

Algorithm
1×egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
049733452
149733452

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 x x) 9/40)
0.0b
(+.f64 -1/2 (*.f64 (*.f64 x x) 9/40))
0.0b
(+.f64 -1/2 (*.f64 (*.f64 x x) 9/40))
0.1b
(*.f64 (*.f64 x x) 9/40)

rewrite12.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
7×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 add-sqr-sqrt_binary64
3×pow-prod-down_binary64 *-un-lft-identity_binary64 cbrt-unprod_binary64 associate-*r*_binary64 add-cube-cbrt_binary64 prod-exp_binary64
1×flip3-+_binary64 associate-*l*_binary64 unswap-sqr_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
2 → 30
Calls

4 calls:

6.0ms
(*.f64 (*.f64 x x) 9/40)
3.0ms
(+.f64 -1/2 (*.f64 (*.f64 x x) 9/40))
0.0ms
(+.f64 -1/2 (*.f64 (*.f64 x x) 9/40))
0.0ms
(*.f64 (*.f64 x x) 9/40)

series71.0ms (0%)

Counts
2 → 9
Calls

2 calls:

45.0ms
(+.f64 -1/2 (*.f64 (*.f64 x x) 9/40))
26.0ms
(*.f64 (*.f64 x x) 9/40)
Compiler

Compiled 95 to 96 computations (-1.1% saved)

simplify100.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
04820387
14820387

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

19.4b
(/.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5))) (-.f64 x (tan.f64 x)))
1.7b
(-.f64 x (tan.f64 x))
0.1b
(*.f64 (pow.f64 x 3) 1/6)
0.1b
(*.f64 1/120 (pow.f64 x 5))
0.1b
(*.f64 (pow.f64 x 3) 1/6)
1.7b
(-.f64 x (tan.f64 x))
19.4b
(/.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5))) (-.f64 x (tan.f64 x)))
19.7b
(-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5)))

rewrite34.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×add-sqr-sqrt_binary64
29×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
15×times-frac_binary64
12×associate-*l*_binary64
11×add-exp-log_binary64
8×add-log-exp_binary64 add-cbrt-cube_binary64
5×associate-/r*_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
4×pow1_binary64 flip3--_binary64 cancel-sign-sub-inv_binary64 unswap-sqr_binary64 unpow-prod-down_binary64 cube-prod_binary64 flip--_binary64
3×associate-*r*_binary64 prod-exp_binary64 associate-/l*_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 sqr-pow_binary64 associate-/r/_binary64
1×pow-to-exp_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 pow-exp_binary64 unpow3_binary64 *-commutative_binary64 cube-mult_binary64
Counts
4 → 99
Calls

8 calls:

10.0ms
(/.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5))) (-.f64 x (tan.f64 x)))
6.0ms
(*.f64 (pow.f64 x 3) 1/6)
5.0ms
(-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5)))
3.0ms
(-.f64 x (tan.f64 x))
0.0ms
(*.f64 1/120 (pow.f64 x 5))

series260.0ms (0.1%)

Counts
4 → 22
Calls

4 calls:

105.0ms
(-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5)))
62.0ms
(-.f64 x (tan.f64 x))
56.0ms
(/.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/120 (pow.f64 x 5))) (-.f64 x (tan.f64 x)))
37.0ms
(*.f64 (pow.f64 x 3) 1/6)
Compiler

Compiled 517 to 433 computations (16.2% saved)

simplify88.0ms (0%)

Algorithm
1×egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049092452
149092452

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (pow.f64 x 3) 1/6)
0.1b
(*.f64 1/120 (pow.f64 x 5))
0.0b
(*.f64 1/5040 (pow.f64 x 7))
0.0b
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9)))
0.3b
(*.f64 1/362880 (pow.f64 x 9))
1.7b
(-.f64 x (tan.f64 x))
18.0b
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
24.9b
(-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9))))

rewrite60.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
54×add-sqr-sqrt_binary64
49×*-un-lft-identity_binary64
25×times-frac_binary64
21×add-cube-cbrt_binary64
18×add-log-exp_binary64
14×difference-of-squares_binary64 distribute-lft-out--_binary64
11×add-exp-log_binary64
8×flip3-+_binary64 add-cbrt-cube_binary64 flip-+_binary64 frac-sub_binary64
7×associate-*r*_binary64
6×associate-/l/_binary64 cancel-sign-sub-inv_binary64
5×associate-/r*_binary64 diff-log_binary64 associate-/l*_binary64
4×pow1_binary64 flip3--_binary64 unpow-prod-down_binary64 flip--_binary64 sum-log_binary64
3×associate-*l*_binary64 unswap-sqr_binary64 prod-exp_binary64
2×sub-neg_binary64 sqr-pow_binary64 associate-/r/_binary64
1×pow-to-exp_binary64 associate--r+_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 pow-exp_binary64 associate--l+_binary64 *-commutative_binary64
Counts
4 → 122
Calls

8 calls:

21.0ms
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
13.0ms
(-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9))))
6.0ms
(*.f64 1/362880 (pow.f64 x 9))
4.0ms
(-.f64 x (tan.f64 x))
0.0ms
(+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9)))

series252.0ms (0.1%)

Counts
4 → 25
Calls

4 calls:

69.0ms
(-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9))))
66.0ms
(-.f64 x (tan.f64 x))
62.0ms
(/.f64 (-.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/6) (*.f64 1/5040 (pow.f64 x 7))) (+.f64 (*.f64 1/120 (pow.f64 x 5)) (*.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
54.0ms
(*.f64 1/362880 (pow.f64 x 9))
Compiler

Compiled 755 to 631 computations (16.4% saved)

simplify139.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
048795774
148795774

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (tan.f64 x) (tan.f64 x))
0.1b
(*.f64 x (tan.f64 x))
0.1b
(+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x))))
0.0b
(+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))
1.7b
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
1.8b
(-.f64 x (sin.f64 x))
5.6b
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
15.4b
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))

rewrite165.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
469×add-sqr-sqrt_binary64
296×*-un-lft-identity_binary64
251×times-frac_binary64
244×difference-of-squares_binary64
147×unpow-prod-down_binary64 cube-prod_binary64
131×associate-*l*_binary64
112×distribute-lft-out--_binary64
97×sqr-pow_binary64
72×add-cube-cbrt_binary64
25×associate-/r*_binary64
15×cancel-sign-sub-inv_binary64
12×difference-cubes_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
6×pow1_binary64
5×flip3--_binary64 associate-/l*_binary64 flip--_binary64
4×associate-/r/_binary64
3×associate-*r*_binary64
2×flip3-+_binary64 associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-*r/_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64 frac-times_binary64
1×pow-prod-down_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 unpow3_binary64 associate-*l/_binary64 *-commutative_binary64 cube-mult_binary64
Counts
4 → 389
Calls

8 calls:

46.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
21.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
19.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
8.0ms
(-.f64 x (sin.f64 x))
0.0ms
(+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))

series534.0ms (0.3%)

Counts
4 → 39
Calls

4 calls:

221.0ms
(*.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
152.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
124.0ms
(/.f64 (-.f64 x (sin.f64 x)) (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
36.0ms
(-.f64 x (sin.f64 x))
Compiler

Compiled 1307 to 842 computations (35.6% saved)

simplify172.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
428 → 428
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0504115319

prune18.1s (10%)

Pruning

391 alts after pruning (385 fresh and 6 done)

PrunedKeptTotal
New546357903
Fresh252853
Picked000
Done066
Total571391962
Error
0b
Counts
962 → 391
Compiler

Compiled 32410 to 17510 computations (46% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

1.7b
(-.f64 x (tan.f64 x))
0.0b
(log.f64 (exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))))
0.0b
(/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))
0.0b
(exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x))))
0.0b
(exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x))))
0.0b
(log.f64 (exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))))
1.7b
(-.f64 x (tan.f64 x))
1.8b
(+.f64 x (neg.f64 (sin.f64 x)))

rewrite48.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
94×*-un-lft-identity_binary64
62×exp-prod_binary64
50×add-sqr-sqrt_binary64 times-frac_binary64
32×log-pow_binary64
28×add-cube-cbrt_binary64
22×distribute-lft-out_binary64
11×add-log-exp_binary64 distribute-rgt-neg-in_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
5×pow1_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 associate-/r/_binary64 exp-diff_binary64 div-sub_binary64
3×associate-+r-_binary64 flip3--_binary64 log-prod_binary64 neg-sub0_binary64 cancel-sign-sub-inv_binary64 flip--_binary64 unsub-neg_binary64
2×div-inv_binary64 log-div_binary64 sum-log_binary64
1×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 rem-log-exp_binary64 rem-exp-log_binary64 neg-log_binary64 +-commutative_binary64 flip-+_binary64
Counts
4 → 118
Calls

8 calls:

14.0ms
(log.f64 (exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))))
12.0ms
(exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x))))
6.0ms
(+.f64 x (neg.f64 (sin.f64 x)))
4.0ms
(-.f64 x (tan.f64 x))
0.0ms
(exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x))))

series512.0ms (0.3%)

Counts
4 → 39
Calls

4 calls:

224.0ms
(log.f64 (exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x)))))
195.0ms
(exp.f64 (/.f64 (+.f64 x (neg.f64 (sin.f64 x))) (-.f64 x (tan.f64 x))))
56.0ms
(-.f64 x (tan.f64 x))
36.0ms
(+.f64 x (neg.f64 (sin.f64 x)))
Compiler

Compiled 1109 to 795 computations (28.3% saved)

simplify65.0ms (0%)

Algorithm
1×egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
056492990

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b
(*.f64 (*.f64 x x) 9/40)
0.1b
(*.f64 (*.f64 x x) 9/40)

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×pow-prod-down_binary64 cbrt-unprod_binary64 associate-*r*_binary64 prod-exp_binary64 add-sqr-sqrt_binary64
2×*-un-lft-identity_binary64 add-cube-cbrt_binary64
1×add-log-exp_binary64 associate-*l*_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
1 → 19
Calls

2 calls:

6.0ms
(*.f64 (*.f64 x x) 9/40)
0.0ms
(*.f64 (*.f64 x x) 9/40)

series25.0ms (0%)

Counts
1 → 3
Calls

1 calls:

25.0ms
(*.f64 (*.f64 x x) 9/40)
Compiler

Compiled 30 to 30 computations (0% saved)

simplify85.0ms (0%)

Algorithm
1×egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
05394182

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x))))))
0.0b
(/.f64 (-.f64 x (sin.f64 x)) (/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x))))
0.0b
(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x)))))
0.0b
(+.f64 x (tan.f64 x))
0.2b
(*.f64 (tan.f64 x) (tan.f64 x))
1.7b
(-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x)))
1.8b
(-.f64 x (sin.f64 x))
14.8b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x)))

rewrite32.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
31×*-un-lft-identity_binary64
23×add-sqr-sqrt_binary64
19×add-cube-cbrt_binary64
16×times-frac_binary64
11×pow1_binary64
8×add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
7×difference-of-squares_binary64
5×distribute-lft-out_binary64
4×associate-/r*_binary64 cancel-sign-sub-inv_binary64 associate-/l*_binary64 tan-quot_binary64
3×flip3--_binary64 swap-sqr_binary64 associate-*r*_binary64 associate-*l*_binary64 flip--_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 associate-/r/_binary64
1×pow-prod-down_binary64 flip3-+_binary64 cbrt-unprod_binary64 pow-prod-up_binary64 cbrt-undiv_binary64 associate-*r/_binary64 pow-plus_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 distribute-lft-out--_binary64 div-inv_binary64 div-exp_binary64 pow-sqr_binary64 flip-+_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 98
Calls

8 calls:

9.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x)))
6.0ms
(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms
(-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x)))
4.0ms
(-.f64 x (sin.f64 x))
0.0ms
(+.f64 x (tan.f64 x))

series356.0ms (0.2%)

Counts
4 → 30
Calls

4 calls:

153.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 x (tan.f64 x)))
106.0ms
(-.f64 (*.f64 x x) (*.f64 (tan.f64 x) (tan.f64 x)))
63.0ms
(*.f64 (tan.f64 x) (tan.f64 x))
33.0ms
(-.f64 x (sin.f64 x))
Compiler

Compiled 852 to 604 computations (29.1% saved)

simplify74.0ms (0%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
052482039

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x))))
0.1b
(*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))
0.0b
(+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))
0.0b
(+.f64 x (sin.f64 x))
1.7b
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
1.8b
(-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x)))
15.4b
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
23.6b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))

rewrite100.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
20×difference-of-squares_binary64
18×add-exp-log_binary64 add-cbrt-cube_binary64
16×associate-/r/_binary64 associate-*l*_binary64
15×unpow-prod-down_binary64 cube-prod_binary64
13×cancel-sign-sub-inv_binary64
12×add-cube-cbrt_binary64
10×frac-times_binary64
9×flip3--_binary64 sqr-pow_binary64 flip--_binary64
8×flip3-+_binary64 add-log-exp_binary64 times-frac_binary64 flip-+_binary64
6×pow1_binary64 associate-*r/_binary64
5×cbrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 associate-*l/_binary64
4×cbrt-undiv_binary64 associate-/l*_binary64 div-exp_binary64
3×associate-*r*_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 div-inv_binary64
1×pow-prod-down_binary64 difference-cubes_binary64 associate-/r*_binary64 associate--r-_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 sqr-sin-a_binary64 unpow3_binary64 *-commutative_binary64 cube-mult_binary64
Counts
4 → 135
Calls

8 calls:

37.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
23.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))
14.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
5.0ms
(-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x)))
0.0ms
(+.f64 x (sin.f64 x))

series675.0ms (0.4%)

Counts
4 → 39
Calls

4 calls:

263.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
190.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))
152.0ms
(-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))
69.0ms
(-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x)))
Compiler

Compiled 1477 to 918 computations (37.8% saved)

simplify74.0ms (0%)

Algorithm
1×egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
051075701

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(log.f64 (exp.f64 (*.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))))
0.0b
(/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x))))
0.0b
(*.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))))
0.0b
(+.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x)))
0.0b
(sqrt.f64 (sin.f64 x))
0.0b
(sqrt.f64 (sin.f64 x))
1.0b
(-.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x)))
1.0b
(-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))

rewrite29.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
18×*-un-lft-identity_binary64
12×cancel-sign-sub-inv_binary64
10×add-cube-cbrt_binary64
8×add-log-exp_binary64 difference-of-squares_binary64
6×pow1_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 distribute-lft-out--_binary64
2×sub-neg_binary64 pow1/2_binary64 flip3--_binary64 diff-log_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip--_binary64
Counts
4 → 72
Calls

8 calls:

7.0ms
(-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))
7.0ms
(-.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x)))
2.0ms
(sqrt.f64 (sin.f64 x))
2.0ms
(sqrt.f64 (sin.f64 x))
0.0ms
(+.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x)))

series118.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

40.0ms
(-.f64 (sqrt.f64 x) (sqrt.f64 (tan.f64 x)))
33.0ms
(-.f64 (sqrt.f64 x) (sqrt.f64 (sin.f64 x)))
23.0ms
(sqrt.f64 (sin.f64 x))
21.0ms
(sqrt.f64 (sin.f64 x))
Compiler

Compiled 815 to 493 computations (39.5% saved)

simplify62.0ms (0%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
05305987

prune28.6s (15.8%)

Pruning

597 alts after pruning (587 fresh and 10 done)

PrunedKeptTotal
New328237565
Fresh30350380
Picked000
Done11011
Total359597956
Error
0b
Counts
956 → 597
Compiler

Compiled 33618 to 16940 computations (49.6% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (-.f64 x (sin.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x)))))
0.0b
(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x))))))
0.0b
(+.f64 x (tan.f64 x))
0.0b
(+.f64 x (tan.f64 x))
0.0b
(/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x)))
0.0b
(/.f64 (+.f64 x (tan.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x))))
1.7b
(-.f64 x (tan.f64 x))
1.8b
(-.f64 x (sin.f64 x))

rewrite75.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
264×*-un-lft-identity_binary64
224×times-frac_binary64
148×add-sqr-sqrt_binary64
94×add-cube-cbrt_binary64
58×distribute-lft-out_binary64
31×associate-/r*_binary64
27×difference-of-squares_binary64 distribute-lft-out--_binary64
13×associate-/r/_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64 flip3--_binary64 associate-/l*_binary64 flip--_binary64
7×div-inv_binary64
6×cancel-sign-sub-inv_binary64
4×associate-/l/_binary64 pow1_binary64 cbrt-undiv_binary64 div-exp_binary64
2×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 clear-num_binary64 frac-2neg_binary64 flip-+_binary64
Counts
4 → 228
Calls

8 calls:

16.0ms
(/.f64 (+.f64 x (tan.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x))))
14.0ms
(/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (tan.f64 x))
0.0ms
(+.f64 x (tan.f64 x))

series280.0ms (0.2%)

Counts
4 → 36
Calls

4 calls:

112.0ms
(/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x)))
72.0ms
(/.f64 (+.f64 x (tan.f64 x)) (/.f64 (+.f64 x (tan.f64 x)) (-.f64 x (tan.f64 x))))
62.0ms
(-.f64 x (tan.f64 x))
34.0ms
(-.f64 x (sin.f64 x))
Compiler

Compiled 1020 to 687 computations (32.6% saved)

simplify118.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049426754
149426754

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 x (*.f64 x 9/40))
0.1b
(*.f64 x 9/40)
0.1b
(*.f64 x 9/40)
0.1b
(*.f64 x (*.f64 x 9/40))

rewrite11.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
9×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
7×add-sqr-sqrt_binary64
6×associate-*l*_binary64
5×*-un-lft-identity_binary64 add-cube-cbrt_binary64
4×pow-prod-down_binary64 cbrt-unprod_binary64 associate-*r*_binary64 prod-exp_binary64
2×add-log-exp_binary64 *-commutative_binary64
1×unswap-sqr_binary64
Counts
2 → 36
Calls

4 calls:

5.0ms
(*.f64 x (*.f64 x 9/40))
4.0ms
(*.f64 x 9/40)
0.0ms
(*.f64 x 9/40)
0.0ms
(*.f64 x (*.f64 x 9/40))

series40.0ms (0%)

Counts
2 → 6
Calls

2 calls:

24.0ms
(*.f64 x (*.f64 x 9/40))
15.0ms
(*.f64 x 9/40)
Compiler

Compiled 60 to 54 computations (10% saved)

simplify75.0ms (0%)

Algorithm
1×egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04986296
14986296

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (-.f64 x (sin.f64 x)))
0.0b
(log.f64 (exp.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 x (tan.f64 x)))))
0.0b
(/.f64 (*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 x (tan.f64 x)))
0.0b
(exp.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 x (tan.f64 x))))
0.2b
(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
1.7b
(-.f64 x (tan.f64 x))
1.8b
(-.f64 x (sin.f64 x))
1.8b
(-.f64 x (sin.f64 x))

rewrite41.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
35×*-un-lft-identity_binary64
30×sqrt-prod_binary64
19×pow1_binary64
15×add-cube-cbrt_binary64
12×swap-sqr_binary64 sqrt-div_binary64
10×add-log-exp_binary64
9×flip3--_binary64 cancel-sign-sub-inv_binary64 distribute-lft-out--_binary64 flip--_binary64
8×pow1/2_binary64 associate-*r*_binary64 associate-*l*_binary64 sqrt-pow1_binary64
7×difference-of-squares_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×pow-prod-up_binary64
4×unswap-sqr_binary64 frac-times_binary64
3×pow-prod-down_binary64 sub-neg_binary64 diff-log_binary64 pow-sqr_binary64
2×associate-*r/_binary64 rem-sqrt-square_binary64 associate-*l/_binary64
1×cbrt-unprod_binary64 rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 prod-exp_binary64 sqr-abs_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 114
Calls

8 calls:

14.0ms
(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
7.0ms
(-.f64 x (tan.f64 x))
4.0ms
(-.f64 x (sin.f64 x))
4.0ms
(-.f64 x (sin.f64 x))
0.0ms
(exp.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x)))) (-.f64 x (tan.f64 x))))

series166.0ms (0.1%)

Counts
4 → 31
Calls

4 calls:

66.0ms
(-.f64 x (tan.f64 x))
34.0ms
(-.f64 x (sin.f64 x))
33.0ms
(-.f64 x (sin.f64 x))
32.0ms
(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
Compiler

Compiled 810 to 569 computations (29.8% saved)

simplify77.0ms (0%)

Algorithm
1×egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050751719

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x)))
0.1b
(*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))
0.0b
(+.f64 (tan.f64 x) x)
0.0b
(+.f64 x (sin.f64 x))
1.8b
(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
11.2b
(log.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x)))))
15.4b
(*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x))))
23.6b
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))

rewrite125.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×add-exp-log_binary64
21×add-sqr-sqrt_binary64
19×associate-*l*_binary64
18×add-cbrt-cube_binary64
16×associate-/r/_binary64 difference-of-squares_binary64
14×times-frac_binary64
12×frac-times_binary64
11×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×flip3-+_binary64 flip-+_binary64
9×pow1_binary64 prod-exp_binary64
8×flip3--_binary64 associate-*r/_binary64 cancel-sign-sub-inv_binary64 flip--_binary64
7×unpow-prod-down_binary64 associate-/l*_binary64
6×add-log-exp_binary64 div-exp_binary64 associate-*l/_binary64
5×cbrt-unprod_binary64 unpow2_binary64 sqr-pow_binary64 log-div_binary64
4×cbrt-undiv_binary64 rem-log-exp_binary64
3×associate-*r*_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 log-pow_binary64 div-inv_binary64
1×associate-/r*_binary64 sub-neg_binary64 diff-log_binary64 log-prod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 127
Calls

8 calls:

42.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x))))
29.0ms
(log.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x)))))
27.0ms
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))
7.0ms
(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
0.0ms
(+.f64 x (sin.f64 x))

series854.0ms (0.5%)

Counts
4 → 34
Calls

4 calls:

408.0ms
(log.f64 (*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x)))))
231.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (*.f64 (tan.f64 x) (+.f64 (tan.f64 x) x))))
165.0ms
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)) (+.f64 x (sin.f64 x))))
49.0ms
(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
Compiler

Compiled 1354 to 931 computations (31.2% saved)

simplify104.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050316665

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))))
0.0b
(*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x)))
0.0b
(+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))
0.0b
(+.f64 x (sin.f64 x))
6.1b
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
6.1b
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
9.0b
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
13.2b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x))))

rewrite190.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
76×sqrt-div_binary64
63×add-sqr-sqrt_binary64
58×frac-times_binary64
52×associate-/r/_binary64
50×sqrt-prod_binary64
39×flip3--_binary64 flip--_binary64
35×difference-of-squares_binary64
34×associate-*l*_binary64
31×*-un-lft-identity_binary64
29×associate-*l/_binary64
27×add-exp-log_binary64 add-cbrt-cube_binary64
24×unpow-prod-down_binary64 cube-prod_binary64
20×flip3-+_binary64 flip-+_binary64
18×associate-*r/_binary64
16×sqr-pow_binary64
11×add-cube-cbrt_binary64
10×cbrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64
8×pow1_binary64 times-frac_binary64
6×cbrt-undiv_binary64 div-exp_binary64
4×add-log-exp_binary64 associate-/l*_binary64
3×associate-*r*_binary64
2×difference-cubes_binary64 associate-/l/_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-inv_binary64
1×pow-prod-down_binary64 associate-/r*_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 190
Calls

8 calls:

64.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
51.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x))))
15.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
14.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
0.0ms
(+.f64 x (sin.f64 x))

series392.0ms (0.2%)

Counts
4 → 24
Calls

4 calls:

191.0ms
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x)))) (+.f64 (*.f64 x x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 x (tan.f64 x)))))
142.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3))) (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))) (+.f64 x (sin.f64 x))))
31.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
29.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 (tan.f64 x) 3)))
Compiler

Compiled 1068 to 662 computations (38% saved)

simplify98.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
050618333

prune59.9s (33%)

Pruning

794 alts after pruning (779 fresh and 15 done)

PrunedKeptTotal
New579247826
Fresh50532582
Picked000
Done01515
Total6297941423
Error
0b
Counts
1423 → 794
Compiler

Compiled 21788 to 7905 computations (63.7% saved)

simplify1.4s (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
0504778600

regimes12.0s (6.6%)

Compiler

Compiled 97886 to 58306 computations (40.4% saved)

bsearch143.0ms (0.1%)

Steps
ItersRangePoint
9
1.748382607301684e-08
1.046740638388904
0.028382328502402018
9
-1365.9006478697752
-0.004972054706718268
-0.03145921990197293
Compiler

Compiled 1 to 1 computations (0% saved)

regimes474.0ms (0.3%)

Compiler

Compiled 2812 to 2218 computations (21.1% saved)

bsearch49.0ms (0%)

Steps
ItersRangePoint
9
1.748382607301684e-08
1.046740638388904
0.028382328502402018
9
-1365.9006478697752
-0.004972054706718268
-0.03145921990197293
Compiler

Compiled 1 to 1 computations (0% saved)

regimes355.0ms (0.2%)

Compiler

Compiled 1854 to 1508 computations (18.7% saved)

bsearch47.0ms (0%)

Steps
ItersRangePoint
9
1.748382607301684e-08
1.046740638388904
0.028382328502402018
9
-1365.9006478697752
-0.004972054706718268
-0.029701072230053045
Compiler

Compiled 1 to 1 computations (0% saved)

regimes129.0ms (0.1%)

Compiler

Compiled 363 to 322 computations (11.3% saved)

bsearch43.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
2.8883948314408894
9
-1365.9006478697752
-0.004972054706718268
-2.7831107132547697
Compiler

Compiled 1 to 1 computations (0% saved)

regimes74.0ms (0%)

Compiler

Compiled 174 to 154 computations (11.5% saved)

bsearch42.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
2.980031341429843
9
-1365.9006478697752
-0.004972054706718268
-2.8536616560145953
Compiler

Compiled 1 to 1 computations (0% saved)

regimes70.0ms (0%)

Compiler

Compiled 161 to 143 computations (11.2% saved)

bsearch40.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
2.6134853014740287
9
-1365.9006478697752
-0.004972054706718268
-2.289254113935988
Compiler

Compiled 1 to 1 computations (0% saved)

regimes352.0ms (0.2%)

Compiler

Compiled 116 to 105 computations (9.5% saved)

bsearch38.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
2.6134853014740287
9
-1365.9006478697752
-0.004972054706718268
-2.289254113935988
Compiler

Compiled 1 to 1 computations (0% saved)

regimes55.0ms (0%)

Compiler

Compiled 110 to 101 computations (8.2% saved)

bsearch38.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
2.6134853014740287
9
-1365.9006478697752
-0.004972054706718268
-2.5714578849752914
Compiler

Compiled 1 to 1 computations (0% saved)

regimes30.0ms (0%)

Accuracy

Total 0.0b remaining (82.9%)

Threshold costs 0.0b (82.9%)

Compiler

Compiled 31 to 30 computations (3.2% saved)

bsearch48.0ms (0%)

Steps
ItersRangePoint
8
1.046740638388904
3637.686101964701
1.5736505708253863
9
-1365.9006478697752
-0.004972054706718268
-1.580219514889386
Compiler

Compiled 259 to 175 computations (32.4% saved)

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0162371
1162371

end0.0ms (0%)

sample49.6s (27.3%)

Algorithm
1×intervals
Results
4.0s1982×body2048valid
1.0s3022×body1024valid
288.0ms1508×body512valid
151.0ms137×body4096valid
97.0ms752×body256valid
47.0ms599×body128valid
Compiler

Compiled 49693 to 29679 computations (40.3% saved)

Pareto

0.9581455082446618

Profiling

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