Details

Time bar (total: 20.0s)

analyze2.9s (14.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample144.0ms (0.7%)

Algorithm
1×intervals
Results
62.0ms74×body1024valid
26.0ms49×body512valid
21.0ms114×body128valid
8.0ms49×body128invalid
7.0ms19×body256valid
2.0ms3×body512invalid
1.0ms4×body256invalid
1.0ms1×body1024invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify189.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
31.5b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
4.0b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
9.6b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.7b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite83.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_116
58×prod-exp_binary64_127
52×add-cbrt-cube_binary64_114
28×times-frac_binary64_84
26×add-sqr-sqrt_binary64_100 cbrt-unprod_binary64_111
24×div-exp_binary64_129
20×pow1_binary64_139
19×*-un-lft-identity_binary64_78
18×associate-*l*_binary64_19
17×add-cube-cbrt_binary64_113
16×associate-*l/_binary64_21
12×associate-/l*_binary64_23
10×unpow-prod-down_binary64_157 frac-times_binary64_88 associate-*r*_binary64_18 pow-prod-down_binary64_149 cube-prod_binary64_106
8×tan-quot_binary64_237 pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-undiv_binary64_112
6×associate-*r/_binary64_20
5×unswap-sqr_binary64_46
4×add-log-exp_binary64_117 flip-+_binary64_52 sqr-pow_binary64_50 flip3-+_binary64_81
3×cube-mult_binary64_108 *-commutative_binary64_9 unpow3_binary64_144
2×div-inv_binary64_75
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 159
Calls

4 calls:

28.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
12.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series910.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

524.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
264.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
96.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
25.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify94.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
055553677

prune401.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1629171
Fresh000
Picked101
Done000
Total1639172
Error
14.0b
Counts
172 → 9
Compiler

Compiled 4993 to 2740 computations (45.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.7b
(*.f64 (/.f64 t l) (sin.f64 k))
8.9b
(/.f64 (*.f64 t t) l)
9.6b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite124.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
120×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
70×cbrt-unprod_binary64_111 prod-exp_binary64_127
44×associate-*l/_binary64_21
34×frac-times_binary64_88
29×pow1_binary64_139
21×add-sqr-sqrt_binary64_100 cbrt-undiv_binary64_112 div-exp_binary64_129
18×*-un-lft-identity_binary64_78
17×pow-prod-down_binary64_149
16×tan-quot_binary64_237 add-cube-cbrt_binary64_113
15×associate-*l*_binary64_19
14×associate-*r/_binary64_20
13×times-frac_binary64_84
10×associate-*r*_binary64_18
8×flip-+_binary64_52 flip3-+_binary64_81
4×add-log-exp_binary64_117
3×*-commutative_binary64_9 associate-/r*_binary64_22
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/l*_binary64_23 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 159
Calls

4 calls:

51.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
28.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
14.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
9.0ms
(/.f64 (*.f64 t t) l)

series967.0ms (4.8%)

Counts
4 → 12
Calls

4 calls:

573.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
297.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
82.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
14.0ms
(/.f64 (*.f64 t t) l)

simplify113.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049814094
149814094

prune381.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1647171
Fresh538
Picked101
Done000
Total17010180
Error
7.3b
Counts
180 → 10
Compiler

Compiled 5198 to 2586 computations (50.3% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
2.7b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.7b
(*.f64 (/.f64 t l) (sin.f64 k))
9.6b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite148.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
151×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
78×cbrt-unprod_binary64_111 prod-exp_binary64_127
76×times-frac_binary64_84
59×associate-*l*_binary64_19
54×add-sqr-sqrt_binary64_100
51×*-un-lft-identity_binary64_78
49×add-cube-cbrt_binary64_113
47×associate-*l/_binary64_21
37×cbrt-undiv_binary64_112 div-exp_binary64_129
35×frac-times_binary64_88
34×pow1_binary64_139
20×pow-prod-down_binary64_149
16×tan-quot_binary64_237
15×associate-*r/_binary64_20
11×associate-*r*_binary64_18
8×flip-+_binary64_52 flip3-+_binary64_81
5×div-inv_binary64_75
4×*-commutative_binary64_9 add-log-exp_binary64_117
2×unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 associate-/r/_binary64_24 distribute-lft-out_binary64_29
Counts
4 → 214
Calls

4 calls:

41.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
35.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
17.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.1s (5.6%)

Counts
4 → 12
Calls

4 calls:

622.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
306.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
107.0ms
(*.f64 (/.f64 t l) (sin.f64 k))
81.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))

simplify163.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
049795442
149795442

prune450.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2197226
Fresh459
Picked101
Done000
Total22412236
Error
4.8b
Counts
236 → 12
Compiler

Compiled 7132 to 3362 computations (52.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
3.7b
(*.f64 (/.f64 t l) (sin.f64 k))
3.7b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
9.1b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))

rewrite159.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
103×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
53×cbrt-unprod_binary64_111 prod-exp_binary64_127
41×times-frac_binary64_84
33×add-sqr-sqrt_binary64_100
30×*-un-lft-identity_binary64_78
29×pow1_binary64_139
28×add-cube-cbrt_binary64_113
27×associate-*r/_binary64_20
26×associate-*l/_binary64_21
23×cbrt-undiv_binary64_112 div-exp_binary64_129
20×associate-*l*_binary64_19
19×frac-times_binary64_88
17×pow-prod-down_binary64_149
14×tan-quot_binary64_237
13×associate-/r*_binary64_22
11×associate-/l/_binary64_25
8×flip-+_binary64_52 flip3-+_binary64_81
5×associate-*r*_binary64_18
4×add-log-exp_binary64_117 div-inv_binary64_75
3×*-commutative_binary64_9
2×unswap-sqr_binary64_46
1×frac-2neg_binary64_89 associate-/l*_binary64_23 associate-/r/_binary64_24 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 169
Calls

4 calls:

47.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
44.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
17.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.3s (6.4%)

Counts
4 → 12
Calls

4 calls:

448.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k)))))
420.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))) (/.f64 l t))
311.0ms
(*.f64 (tan.f64 k) (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))))
96.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify106.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051325062

prune345.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1765181
Fresh3811
Picked101
Done000
Total18013193
Error
3.1b
Counts
193 → 13
Compiler

Compiled 5599 to 2170 computations (61.2% saved)

regimes1.9s (9.2%)

Accuracy

Total 3.9b remaining (46.8%)

Threshold costs 0b (0%)

Compiler

Compiled 13091 to 9961 computations (23.9% saved)

bsearch264.0ms (1.3%)

Steps
ItersRangePoint
10
3.9433422968649473e-72
1.195302319374534e-60
2.836626806641897e-62
9
-6.582993984515394e-49
-6.790933101523139e-54
-3.052236327539236e-50
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04993
14993

end0.0ms (0%)

sample7.8s (38.7%)

Algorithm
1×intervals
Results
2.1s2671×body1024valid
713.0ms1280×body512valid
659.0ms3460×body128valid
273.0ms1479×body128invalid
227.0ms585×body256valid
87.0ms152×body512invalid
44.0ms63×body1024invalid
41.0ms114×body256invalid
5.0ms4×body2048valid
Compiler

Compiled 2171 to 1646 computations (24.2% saved)

Profiling

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