Details

Time bar (total: 49.5s)

analyze543.0ms (1.1%)

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
12.5%87.4%0.1%6
34.3%65.5%0.1%7
46.8%53%0.1%8
48%51.9%0.1%9
63%36.9%0.1%10
71.7%28.2%0.1%11
72%27.8%0.1%12
80.5%19.4%0.1%13
85.4%14.5%0.1%14
Compiler

Compiled 10 to 9 computations (10% saved)

sample37.0ms (0.1%)

Algorithm
1×intervals
Results
12.0ms46×body1024valid
11.0ms179×body128valid
3.0ms18×body512valid
2.0ms13×body256valid
Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify101.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02014
12014

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 9 to 8 computations (11.1% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 z (cos.f64 y))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170
4×pow1_binary64_4231 add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206 add-log-exp_binary64_4209 add-cube-cbrt_binary64_4205
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 flip-+_binary64_4144 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 sum-log_binary64_4261 pow-prod-down_binary64_4241 distribute-lft-out_binary64_4121 unswap-sqr_binary64_4138
Counts
2 → 30
Calls

4 calls:

5.0ms
(*.f64 z (cos.f64 y))
4.0ms
(+.f64 x (sin.f64 y))
0.0ms
(+.f64 x (sin.f64 y))
0.0ms
(*.f64 z (cos.f64 y))

series132.0ms (0.3%)

Counts
2 → 20
Calls

2 calls:

71.0ms
(*.f64 z (cos.f64 y))
62.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 319 to 281 computations (11.9% saved)

simplify88.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
04918436
14918436

prune133.0ms (0.3%)

Pruning

28 alts after pruning (27 fresh and 1 done)

PrunedKeptTotal
New232750
Fresh000
Picked000
Done011
Total232851
Error
0.0b
Counts
51 → 28
Compiler

Compiled 829 to 433 computations (47.8% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 z (cos.f64 y))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170
4×pow1_binary64_4231 add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206 add-log-exp_binary64_4209 add-cube-cbrt_binary64_4205
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 flip-+_binary64_4144 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 sum-log_binary64_4261 pow-prod-down_binary64_4241 distribute-lft-out_binary64_4121 unswap-sqr_binary64_4138
Counts
2 → 30
Calls

4 calls:

4.0ms
(*.f64 z (cos.f64 y))
4.0ms
(+.f64 x (sin.f64 y))
0.0ms
(+.f64 x (sin.f64 y))
0.0ms
(*.f64 z (cos.f64 y))

series133.0ms (0.3%)

Counts
2 → 20
Calls

2 calls:

77.0ms
(*.f64 z (cos.f64 y))
56.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 381 to 343 computations (10% saved)

simplify92.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
04918436
14918436

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.1b
(*.f64 z (cos.f64 y))

rewrite5.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
5×add-sqr-sqrt_binary64_4192
3×pow1_binary64_4231 associate-*l*_binary64_4111 add-exp-log_binary64_4208 *-un-lft-identity_binary64_4170 associate-*r*_binary64_4110 add-cbrt-cube_binary64_4206 add-cube-cbrt_binary64_4205
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 *-commutative_binary64_4101 pow-prod-down_binary64_4241 add-log-exp_binary64_4209 unswap-sqr_binary64_4138
Counts
1 → 18
Calls

2 calls:

4.0ms
(*.f64 z (cos.f64 y))
0.0ms
(*.f64 z (cos.f64 y))

series70.0ms (0.1%)

Counts
1 → 9
Calls

1 calls:

70.0ms
(*.f64 z (cos.f64 y))
Compiler

Compiled 120 to 112 computations (6.7% saved)

simplify142.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 0 (134.0ms)

IterNodesCost
04763253
14763253

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

12.2b
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
1.9b
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
0.1b
(*.f64 1/24 (pow.f64 y 4))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 1/24 (pow.f64 y 4))
1.9b
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
12.2b
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))

rewrite31.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64_4192
11×add-exp-log_binary64_4208 *-un-lft-identity_binary64_4170 add-log-exp_binary64_4209
10×associate-*r*_binary64_4110
9×add-cube-cbrt_binary64_4205
8×add-cbrt-cube_binary64_4206
6×pow1_binary64_4231 associate-*l*_binary64_4111
4×prod-exp_binary64_4219 unpow-prod-down_binary64_4249 sum-log_binary64_4261 unswap-sqr_binary64_4138
3×flip-+_binary64_4144 flip3-+_binary64_4173
2×associate-*r/_binary64_4112 sqr-pow_binary64_4142 cbrt-unprod_binary64_4203 +-commutative_binary64_4100 *-commutative_binary64_4101
1×distribute-lft-in_binary64_4119 pow-to-exp_binary64_4239 distribute-rgt-in_binary64_4120 pow-exp_binary64_4238 pow-prod-down_binary64_4241 associate-+l+_binary64_4103 distribute-lft-out_binary64_4121
Counts
4 → 72
Calls

8 calls:

8.0ms
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
6.0ms
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
6.0ms
(*.f64 1/24 (pow.f64 y 4))
4.0ms
(+.f64 x (sin.f64 y))
0.0ms
(+.f64 x (sin.f64 y))

series288.0ms (0.6%)

Counts
4 → 28
Calls

4 calls:

147.0ms
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
63.0ms
(+.f64 x (sin.f64 y))
41.0ms
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
37.0ms
(*.f64 1/24 (pow.f64 y 4))
Compiler

Compiled 834 to 725 computations (13.1% saved)

simplify107.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (88.0ms)

IterNodesCost
049471543
149471543

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

3.9b
(log.f64 (exp.f64 (+.f64 x (sin.f64 y))))
0.1b
(*.f64 z (cos.f64 y))
0.0b
(exp.f64 (+.f64 x (sin.f64 y)))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(exp.f64 (+.f64 x (sin.f64 y)))
0.1b
(*.f64 z (cos.f64 y))
3.9b
(log.f64 (exp.f64 (+.f64 x (sin.f64 y))))

rewrite24.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
15×*-un-lft-identity_binary64_4170
11×add-sqr-sqrt_binary64_4192
9×add-log-exp_binary64_4209 add-cube-cbrt_binary64_4205
8×exp-prod_binary64_4222
7×pow1_binary64_4231
6×add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206
5×log-pow_binary64_4259
4×log-prod_binary64_4256
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110 distribute-lft-out_binary64_4121
2×sum-log_binary64_4261 rem-exp-log_binary64_4210 exp-sum_binary64_4216
1×rem-log-exp_binary64_4211 prod-exp_binary64_4219 cbrt-unprod_binary64_4203 flip-+_binary64_4144 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 pow-prod-down_binary64_4241 unswap-sqr_binary64_4138
Counts
4 → 61
Calls

8 calls:

6.0ms
(+.f64 x (sin.f64 y))
5.0ms
(log.f64 (exp.f64 (+.f64 x (sin.f64 y))))
5.0ms
(exp.f64 (+.f64 x (sin.f64 y)))
4.0ms
(*.f64 z (cos.f64 y))
0.0ms
(+.f64 x (sin.f64 y))

series370.0ms (0.7%)

Counts
4 → 37
Calls

4 calls:

197.0ms
(log.f64 (exp.f64 (+.f64 x (sin.f64 y))))
73.0ms
(*.f64 z (cos.f64 y))
51.0ms
(exp.f64 (+.f64 x (sin.f64 y)))
50.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 764 to 665 computations (13% saved)

simplify91.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
04921849
14921849

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.3b
(*.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cos.f64 y) (cbrt.f64 z)))
0.1b
(*.f64 (cos.f64 y) (cbrt.f64 z))
0.0b
(+.f64 x (sin.f64 y))
0.5b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b
(cbrt.f64 z)
0.6b
(cbrt.f64 z)
0.6b
(cbrt.f64 z)

rewrite18.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod_binary64_4201
23×add-sqr-sqrt_binary64_4192
15×*-un-lft-identity_binary64_4170 add-cube-cbrt_binary64_4205
11×pow1_binary64_4231
9×pow1/3_binary64_4252
6×swap-sqr_binary64_4137 associate-*l*_binary64_4111 add-exp-log_binary64_4208 associate-*r*_binary64_4110
4×add-cbrt-cube_binary64_4206 add-log-exp_binary64_4209 unswap-sqr_binary64_4138
2×pow-prod-up_binary64_4240 pow-prod-down_binary64_4241 pow-sqr_binary64_4143
1×pow-plus_binary64_4233 prod-exp_binary64_4219 cbrt-unprod_binary64_4203 pow2_binary64_4251 *-commutative_binary64_4101
Counts
4 → 73
Calls

8 calls:

8.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)
0.0ms
(+.f64 x (sin.f64 y))

series324.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

91.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
80.0ms
(cbrt.f64 z)
77.0ms
(cbrt.f64 z)
75.0ms
(cbrt.f64 z)
Compiler

Compiled 442 to 358 computations (19% saved)

simplify79.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
04873548
14873548

prune3.6s (7.3%)

Pruning

167 alts after pruning (162 fresh and 5 done)

PrunedKeptTotal
New216144360
Fresh41822
Picked000
Done156
Total221167388
Error
0.0b
Counts
388 → 167
Compiler

Compiled 7726 to 4309 computations (44.2% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 z (cos.f64 y))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170
4×pow1_binary64_4231 add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206 add-log-exp_binary64_4209 add-cube-cbrt_binary64_4205
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 flip-+_binary64_4144 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 sum-log_binary64_4261 pow-prod-down_binary64_4241 distribute-lft-out_binary64_4121 unswap-sqr_binary64_4138
Counts
2 → 30
Calls

4 calls:

4.0ms
(*.f64 z (cos.f64 y))
4.0ms
(+.f64 x (sin.f64 y))
0.0ms
(+.f64 x (sin.f64 y))
0.0ms
(*.f64 z (cos.f64 y))

series132.0ms (0.3%)

Counts
2 → 20
Calls

2 calls:

73.0ms
(*.f64 z (cos.f64 y))
59.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 412 to 374 computations (9.2% saved)

simplify87.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
04918436
14918436

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize27.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 1/6 (pow.f64 y 3))
0.1b
(*.f64 1/24 (pow.f64 y 4))
0.1b
(*.f64 1/120 (pow.f64 y 5))
0.0b
(-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3)))
1.9b
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
9.3b
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))))
12.2b
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
17.7b
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))

rewrite50.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
32×add-log-exp_binary64_4209
15×sum-log_binary64_4261
8×add-sqr-sqrt_binary64_4192 flip-+_binary64_4144 flip3-+_binary64_4173
6×pow1_binary64_4231 associate-*r/_binary64_4112 add-exp-log_binary64_4208 *-un-lft-identity_binary64_4170 add-cbrt-cube_binary64_4206 add-cube-cbrt_binary64_4205
5×associate-+l+_binary64_4103
4×diff-log_binary64_4262 frac-add_binary64_4178
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110 associate-+l-_binary64_4105 +-commutative_binary64_4100
2×distribute-lft-in_binary64_4119 distribute-rgt-in_binary64_4120 associate-+r+_binary64_4102
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 associate--l+_binary64_4107 *-commutative_binary64_4101 cancel-sign-sub-inv_binary64_4136 pow-prod-down_binary64_4241 sub-neg_binary64_4163 unswap-sqr_binary64_4138
Counts
4 → 74
Calls

8 calls:

16.0ms
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))))
10.0ms
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))
8.0ms
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
6.0ms
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
0.0ms
(-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3)))

series859.0ms (1.7%)

Counts
4 → 55
Calls

4 calls:

491.0ms
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))))
167.0ms
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))
156.0ms
(*.f64 z (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
44.0ms
(+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))
Compiler

Compiled 1813 to 1566 computations (13.6% saved)

simplify87.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049314200
149314200

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.0b
(sqrt.f64 (*.f64 z (cos.f64 y)))
0.0b
(sqrt.f64 (*.f64 z (cos.f64 y)))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(sqrt.f64 (*.f64 z (cos.f64 y)))
0.1b
(*.f64 z (cos.f64 y))
0.1b
(*.f64 z (cos.f64 y))
0.3b
(*.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))

rewrite32.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
60×pow1_binary64_4231
30×sqrt-pow1_binary64_4188
23×pow-prod-down_binary64_4241
18×add-sqr-sqrt_binary64_4192
12×*-un-lft-identity_binary64_4170 add-cube-cbrt_binary64_4205
11×pow1/2_binary64_4250
10×associate-*l*_binary64_4111 add-exp-log_binary64_4208 associate-*r*_binary64_4110 add-cbrt-cube_binary64_4206 pow-prod-up_binary64_4240
6×pow-sqr_binary64_4143
5×sqrt-prod_binary64_4186
4×swap-sqr_binary64_4137 add-log-exp_binary64_4209
3×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 *-commutative_binary64_4101 unswap-sqr_binary64_4138
1×pow-plus_binary64_4233 pow2_binary64_4251 sqrt-unprod_binary64_4190 rem-square-sqrt_binary64_4182
Counts
4 → 96
Calls

8 calls:

12.0ms
(*.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))
4.0ms
(*.f64 z (cos.f64 y))
4.0ms
(*.f64 z (cos.f64 y))
3.0ms
(sqrt.f64 (*.f64 z (cos.f64 y)))
0.0ms
(+.f64 x (sin.f64 y))

series295.0ms (0.6%)

Counts
4 → 33
Calls

4 calls:

81.0ms
(*.f64 z (cos.f64 y))
73.0ms
(*.f64 z (cos.f64 y))
71.0ms
(*.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y))))
70.0ms
(sqrt.f64 (*.f64 z (cos.f64 y)))
Compiler

Compiled 1002 to 784 computations (21.8% saved)

simplify72.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049601025
149601025

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
0.0b
(sqrt.f64 (cos.f64 y))
0.0b
(sqrt.f64 (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(sqrt.f64 (cos.f64 y))
0.1b
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
0.1b
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
0.2b
(*.f64 (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))))

rewrite42.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
68×pow1_binary64_4231
41×pow-prod-down_binary64_4241
30×add-sqr-sqrt_binary64_4192
23×sqrt-prod_binary64_4186
21×pow1/2_binary64_4250 sqrt-pow1_binary64_4188
20×add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206
13×associate-*l*_binary64_4111 *-un-lft-identity_binary64_4170 associate-*r*_binary64_4110 add-cube-cbrt_binary64_4205
10×prod-exp_binary64_4219 cbrt-unprod_binary64_4203
8×pow-prod-up_binary64_4240 unswap-sqr_binary64_4138
7×sqrt-unprod_binary64_4190
6×pow-sqr_binary64_4143
4×add-log-exp_binary64_4209
3×*-commutative_binary64_4101
2×pow-plus_binary64_4233
1×swap-sqr_binary64_4137 pow2_binary64_4251 rem-square-sqrt_binary64_4182 rem-sqrt-square_binary64_4183
Counts
4 → 117
Calls

8 calls:

15.0ms
(*.f64 (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))))
7.0ms
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
7.0ms
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
1.0ms
(sqrt.f64 (cos.f64 y))
0.0ms
(+.f64 x (sin.f64 y))

series248.0ms (0.5%)

Counts
4 → 30
Calls

4 calls:

80.0ms
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
74.0ms
(*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y)))
69.0ms
(*.f64 (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (cos.f64 y))))
26.0ms
(sqrt.f64 (cos.f64 y))
Compiler

Compiled 1077 to 845 computations (21.5% saved)

simplify119.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (97.0ms)

IterNodesCost
046701427
146701427

prune9.4s (19%)

Pruning

280 alts after pruning (271 fresh and 9 done)

PrunedKeptTotal
New333122455
Fresh8149157
Picked000
Done1910
Total342280622
Error
0.0b
Counts
622 → 280
Compiler

Compiled 13901 to 8721 computations (37.3% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 z (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 z (cos.f64 y))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170
4×pow1_binary64_4231 add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206 add-log-exp_binary64_4209 add-cube-cbrt_binary64_4205
3×associate-*l*_binary64_4111 associate-*r*_binary64_4110
1×prod-exp_binary64_4219 cbrt-unprod_binary64_4203 flip-+_binary64_4144 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 sum-log_binary64_4261 pow-prod-down_binary64_4241 distribute-lft-out_binary64_4121 unswap-sqr_binary64_4138
Counts
2 → 30
Calls

4 calls:

4.0ms
(*.f64 z (cos.f64 y))
4.0ms
(+.f64 x (sin.f64 y))
0.0ms
(+.f64 x (sin.f64 y))
0.0ms
(*.f64 z (cos.f64 y))

series139.0ms (0.3%)

Counts
2 → 20
Calls

2 calls:

77.0ms
(*.f64 z (cos.f64 y))
62.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 443 to 405 computations (8.6% saved)

simplify88.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
04918436
14918436

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

38.3b
(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
0.1b
(pow.f64 (*.f64 z (cos.f64 y)) 3)
0.1b
(*.f64 z (cos.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.0b
(+.f64 x (sin.f64 y))
0.1b
(*.f64 z (cos.f64 y))
0.1b
(pow.f64 (*.f64 z (cos.f64 y)) 3)
38.3b
(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))

rewrite19.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170
9×pow1_binary64_4231 add-exp-log_binary64_4208 add-cbrt-cube_binary64_4206
8×add-cube-cbrt_binary64_4205 cbrt-prod_binary64_4201
6×add-log-exp_binary64_4209
3×pow-unpow_binary64_4247 associate-*l*_binary64_4111 associate-*r*_binary64_4110
2×prod-exp_binary64_4219 cube-mult_binary64_4200 sqr-pow_binary64_4142 cbrt-unprod_binary64_4203 pow-exp_binary64_4238 cube-prod_binary64_4198 unpow-prod-down_binary64_4249 pow-pow_binary64_4242 unpow3_binary64_4236 rem-cube-cbrt_binary64_4193 pow-prod-down_binary64_4241
1×pow-to-exp_binary64_4239 pow1/3_binary64_4252 flip-+_binary64_4144 rem-cbrt-cube_binary64_4194 +-commutative_binary64_4100 flip3-+_binary64_4173 *-commutative_binary64_4101 sum-log_binary64_4261 distribute-lft-out_binary64_4121 unswap-sqr_binary64_4138
Counts
4 → 69
Calls

8 calls:

4.0ms
(*.f64 z (cos.f64 y))
4.0ms
(pow.f64 (*.f64 z (cos.f64 y)) 3)
3.0ms
(+.f64 x (sin.f64 y))
2.0ms
(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
0.0ms
(+.f64 x (sin.f64 y))

series361.0ms (0.7%)

Counts
4 → 37
Calls

4 calls:

150.0ms
(pow.f64 (*.f64 z (cos.f64 y)) 3)
79.0ms
(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
73.0ms
(*.f64 z (cos.f64 y))
59.0ms
(+.f64 x (sin.f64 y))
Compiler

Compiled 820 to 738 computations (10% saved)

simplify68.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049821008
149821008

localize25.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 1/24 (pow.f64 y 4))
0.1b
(*.f64 1/120 (pow.f64 y 5))
0.1b
(pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3)
0.0b
(-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3)))
6.0b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))
9.3b
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))))
12.2b
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
17.7b
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))

rewrite55.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
32×add-log-exp_binary64_4209
15×sum-log_binary64_4261
12×cbrt-prod_binary64_4201
8×flip-+_binary64_4144 flip3-+_binary64_4173
7×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170 add-cube-cbrt_binary64_4205
6×cube-div_binary64_4199 cbrt-div_binary64_4202
4×pow1_binary64_4231 associate-*r/_binary64_4112 add-exp-log_binary64_4208 diff-log_binary64_4262 add-cbrt-cube_binary64_4206 associate-+l+_binary64_4103 frac-add_binary64_4178
3×associate-+l-_binary64_4105 cube-prod_binary64_4198 unpow-prod-down_binary64_4249 +-commutative_binary64_4100
1×pow1/3_binary64_4252 cube-mult_binary64_4200 sqr-pow_binary64_4142 rem-cbrt-cube_binary64_4194 associate--l+_binary64_4107 associate-+r+_binary64_4102 unpow3_binary64_4236 cancel-sign-sub-inv_binary64_4136 sub-neg_binary64_4163
Counts
4 → 73
Calls

8 calls:

14.0ms
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))))
10.0ms
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))
9.0ms
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
9.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))
0.0ms
(-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3)))

series756.0ms (1.5%)

Counts
4 → 51
Calls

4 calls:

494.0ms
(+.f64 (+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5))) (*.f64 z (cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))))
176.0ms
(+.f64 (-.f64 (+.f64 y x) (*.f64 1/6 (pow.f64 y 3))) (*.f64 1/120 (pow.f64 y 5)))
44.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))) 3))
43.0ms
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
Compiler

Compiled 1708 to 1492 computations (12.6% saved)

simplify112.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049294155
149294155

localize29.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 1/24 (pow.f64 y 4))
0.1b
(*.f64 (cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))) (cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))))
0.1b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))) (cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))) z) (cbrt.f64 (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2))))
0.0b
(+.f64 x (sin.f64 y))
12.2b
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
12.8b
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
12.8b
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
12.8b
(cbrt.f64 (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))

rewrite39.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×add-log-exp_binary64_4209 cbrt-prod_binary64_4201
7×add-sqr-sqrt_binary64_4192 *-un-lft-identity_binary64_4170 add-cube-cbrt_binary64_4205
6×cbrt-div_binary64_4202
4×pow1_binary64_4231 add-exp-log_binary64_4208 flip-+_binary64_4144 add-cbrt-cube_binary64_4206 flip3-+_binary64_4173
3×pow1/3_binary64_4252 sum-log_binary64_4261
1×+-commutative_binary64_4100 associate-+r+_binary64_4102
Counts
4 → 52
Calls

8 calls:

9.0ms
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
8.0ms
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
7.0ms
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
6.0ms
(cbrt.f64 (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
0.0ms
(+.f64 x (sin.f64 y))

series263.0ms (0.5%)

Counts
4 → 20
Calls

4 calls:

75.0ms
(cbrt.f64 (+.f64 (+.f64 1 (*.f64 1/24 (pow.f64 y 4))) (*.f64 (*.f64 y y) -1/2)))
70.0ms
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
70.0ms
(cbrt.f64 (+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4)))))
48.0ms
(+.f64 (*.f64 (*.f64 y y) -1/2) (+.f64 1 (*.f64 1/24 (pow.f64 y 4))))
Compiler

Compiled 1636 to 1359 computations (16.9% saved)

simplify122.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
048921766
148921766

prune11.5s (23.2%)

Pruning

391 alts after pruning (380 fresh and 11 done)

PrunedKeptTotal
New228124352
Fresh10256266
Picked000
Done31114
Total241391632
Error
0.0b
Counts
632 → 391
Compiler

Compiled 8600 to 5520 computations (35.8% saved)

simplify404.0ms (0.8%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0498128553
1498128553

regimes4.2s (8.5%)

Compiler

Compiled 50444 to 39582 computations (21.5% saved)

bsearch0.0ms (0%)

regimes182.0ms (0.4%)

Compiler

Compiled 591 to 567 computations (4.1% saved)

bsearch53.0ms (0.1%)

Steps
ItersRangePoint
9
0.022681178474261755
5178.545978645254
2.4366664959982
9
-8.233717504612026e+35
-3.021181580436474e+29
-3.05419162062594e+29
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes56.0ms (0.1%)

Compiler

Compiled 198 to 225 computations (-13.6% saved)

bsearch0.0ms (0%)

regimes80.0ms (0.2%)

Compiler

Compiled 180 to 207 computations (-15% saved)

bsearch46.0ms (0.1%)

Steps
ItersRangePoint
8
1.1378075031775414e-26
9.25102894020936e-23
9.116748594821486e-23
9
-45339.10329042304
-0.0028392171057893168
-4.720387941625385
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes61.0ms (0.1%)

Compiler

Compiled 75 to 117 computations (-56% saved)

bsearch45.0ms (0.1%)

Steps
ItersRangePoint
8
5.0643402523399674e+39
4.209664799702149e+42
8.891347185406104e+39
9
-1010211632175.9141
-5873620.956831668
-2512680010.260134
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.1%)

Compiler

Compiled 27 to 75 computations (-177.8% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.1%)

Accuracy

Total 0.0b remaining (87.9%)

Threshold costs 0.0b (87.9%)

Compiler

Compiled 18 to 63 computations (-250% saved)

bsearch6.0ms (0%)

Compiler

Compiled 91 to 63 computations (30.8% saved)

simplify5.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
056122
156122

end0.0ms (0%)

sample12.7s (25.6%)

Algorithm
1×intervals
Results
378.0ms1345×body1024valid
363.0ms5664×body128valid
120.0ms648×body512valid
56.0ms341×body256valid
1.0ms2×body2048valid
Compiler

Compiled 12861 to 10097 computations (21.5% saved)

Pareto

0.542389758410344

Profiling

Loading profile data...