Details

analyze666.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample201.0ms (0.3%)

Algorithm

1×

intervals

Results

85.0ms	51×	body	8192	exit
52.0ms	127×	body	1024	valid
15.0ms	57×	body	1024	nan
14.0ms	59×	body	512	valid
6.0ms	11×	body	2048	valid
5.0ms	28×	body	512	nan
5.0ms	34×	body	256	valid
2.0ms	25×	body	128	valid
1.0ms	10×	body	256	nan
1.0ms	11×	body	128	nan

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify208.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

3 → 3

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4785	17
1	4785	17

prune10.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Kept	Total
New	3	3
Fresh	3	3
Picked	0	0
Done	0	0
Total	6	6

Error

19.6b

Counts

6 → 4

Compiler

Compiled 11 to 8 computations (27.3% saved)

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0b	(sqrt.f64 (cos.f64 x))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1123`
12×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
5×	`add-cbrt-cube_binary64_1137`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162`
3×	`add-log-exp_binary64_1140` `sqrt-prod_binary64_1117` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

3 → 47

Calls

6 calls:

4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0ms	(sqrt.f64 (cos.f64 x))

series84.0ms (0.1%)

Counts

3 → 15

Calls

3 calls:

48.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
23.0ms	(sqrt.f64 (cos.f64 x))
13.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 280 to 178 computations (36.4% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5248	1052

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
0.0b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
5×	`add-cbrt-cube_binary64_1137`
4×	`add-exp-log_binary64_1139`
3×	`add-log-exp_binary64_1140` `sqrt-prod_binary64_1117` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`associate-*r/_binary64_1043` `exp-neg_binary64_1148`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sqrt-pow1_binary64_1119` `exp-diff_binary64_1149` `neg-sub0_binary64_1096` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181` `un-div-inv_binary64_1099`

Counts

3 → 41

Calls

6 calls:

7.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series79.0ms (0.1%)

Counts

3 → 15

Calls

3 calls:

42.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
23.0ms	(sqrt.f64 (cos.f64 x))
13.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 300 to 216 computations (28% saved)

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5105	759

prune693.0ms (0.9%)

Pruning

61 alts after pruning (59 fresh and 2 done)

	Pruned	Kept	Total
New	61	57	118
Fresh	0	2	2
Picked	0	0	0
Done	0	2	2
Total	61	61	122

Error

19.6b

Counts

122 → 61

Compiler

Compiled 2149 to 848 computations (60.5% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

2.5b	(log.f64 (sqrt.f64 (cos.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
0.0b	(exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))
0.0b	(sqrt.f64 (cos.f64 x))
2.5b	(log.f64 (sqrt.f64 (cos.f64 x)))
3.6b	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (sqrt.f64 (cos.f64 x)))))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64_1187`
11×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`pow1_binary64_1162` `sqrt-prod_binary64_1117`
6×	`exp-sum_binary64_1147` `exp-prod_binary64_1153` `log-pow_binary64_1190`
5×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
1×	`rem-sqrt-square_binary64_1114` `rem-exp-log_binary64_1141` `rem-log-exp_binary64_1142`

Counts

4 → 57

Calls

8 calls:

4.0ms	(exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(log.f64 (sqrt.f64 (cos.f64 x)))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (sqrt.f64 (cos.f64 x)))))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

series197.0ms (0.3%)

Counts

4 → 21

Calls

4 calls:

82.0ms	(log.f64 (sqrt.f64 (cos.f64 x)))
71.0ms	(exp.f64 (log.f64 (sqrt.f64 (cos.f64 x))))
27.0ms	(sqrt.f64 (cos.f64 x))
15.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (sqrt.f64 (cos.f64 x)))))

Compiler

Compiled 421 to 321 computations (23.8% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4938	799
1	4938	799

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

3.6b	(fmod.f64 (exp.f64 x) 1)
0.0b	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
3.6b	(fmod.f64 (exp.f64 x) 1)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
4×	`add-cbrt-cube_binary64_1137`
3×	`add-exp-log_binary64_1139` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 34

Calls

4 calls:

4.0ms	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) 1)

series51.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

42.0ms	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
8.0ms	(fmod.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 102 computations (27.1% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5246	678

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6)))))) (exp.f64 x))
0.0b	(+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6))))
0.0b	(.f64 1/4 (.f64 x x))
0.0b	(+.f64 (.f64 1/4 (.f64 x x)) (*.f64 19/5760 (pow.f64 x 6)))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6)))))) (exp.f64 x))
0.1b	(*.f64 19/5760 (pow.f64 x 6))
0.1b	(*.f64 1/96 (pow.f64 x 4))
3.6b	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6))))))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1123`
18×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`add-exp-log_binary64_1139`
14×	`associate-r_binary64_1041`
10×	`add-cbrt-cube_binary64_1137`
9×	`times-frac_binary64_1107`
8×	`unpow-prod-down_binary64_1180`
6×	`prod-exp_binary64_1150` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `sqr-pow_binary64_1073`
3×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`*-commutative_binary64_1032` `pow-exp_binary64_1169` `cbrt-unprod_binary64_1134` `pow-to-exp_binary64_1170`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

4 → 84

Calls

8 calls:

6.0ms	(*.f64 19/5760 (pow.f64 x 6))
6.0ms	(*.f64 1/96 (pow.f64 x 4))
4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6)))))) (exp.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6))))))
0.0ms	(+.f64 (.f64 1/4 (.f64 x x)) (*.f64 19/5760 (pow.f64 x 6)))

series207.0ms (0.3%)

Counts

4 → 15

Calls

4 calls:

101.0ms	(/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6)))))) (exp.f64 x))
38.0ms	(*.f64 19/5760 (pow.f64 x 6))
36.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 1/96 (pow.f64 x 4)) (+.f64 (.f64 1/4 (.f64 x x)) (.f64 19/5760 (pow.f64 x 6))))))
32.0ms	(*.f64 1/96 (pow.f64 x 4))

Compiler

Compiled 800 to 630 computations (21.3% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5060	2699

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1123` `times-frac_binary64_1107`
35×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
32×	`cbrt-prod_binary64_1132`
26×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
7×	`add-cbrt-cube_binary64_1137`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`pow-unpow_binary64_1178` `sqrt-prod_binary64_1117`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `cube-div_binary64_1130` `unpow3_binary64_1167` `sqr-pow_binary64_1073`
1×	`rem-sqrt-square_binary64_1114` `pow1/3_binary64_1183` `pow-pow_binary64_1173` `sqrt-pow1_binary64_1119` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow-to-exp_binary64_1170` `cbrt-div_binary64_1133` `pow1/2_binary64_1181` `rem-cbrt-cube_binary64_1125`

Counts

4 → 108

Calls

8 calls:

6.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
6.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

series225.0ms (0.3%)

Counts

4 → 21

Calls

4 calls:

141.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
48.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
23.0ms	(sqrt.f64 (cos.f64 x))
13.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 498 to 338 computations (32.1% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5262	2864

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
0.0b	(/.f64 (*.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
0.0b	(sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
0.0b	(sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(sqrt.f64 (cos.f64 x))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`

Counts

4 → 40

Calls

8 calls:

2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))

series82.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

28.0ms	(sqrt.f64 (cos.f64 x))
26.0ms	(sqrt.f64 (cos.f64 x))
14.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
13.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 560 to 308 computations (45% saved)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4880	582
1	4880	582

prune6.8s (9%)

Pruning

206 alts after pruning (199 fresh and 7 done)

	Pruned	Kept	Total
New	253	154	407
Fresh	9	45	54
Picked	0	0	0
Done	0	7	7
Total	262	206	468

Error

19.6b

Counts

468 → 206

Compiler

Compiled 10564 to 5883 computations (44.3% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3))
0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)
0.0b	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite52.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`cbrt-prod_binary64_1132`
116×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
72×	`times-frac_binary64_1107`
69×	`add-sqr-sqrt_binary64_1123`
68×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`div-inv_binary64_1098`
7×	`add-exp-log_binary64_1139`
6×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `unpow3_binary64_1167` `sqr-pow_binary64_1073`
5×	`pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
4×	`add-log-exp_binary64_1140` `cube-div_binary64_1130`
3×	`pow-unpow_binary64_1178` `sqrt-prod_binary64_1117`
2×	`pow-to-exp_binary64_1170` `cbrt-div_binary64_1133`
1×	`rem-cube-cbrt_binary64_1124` `rem-sqrt-square_binary64_1114` `pow1/3_binary64_1183` `pow-pow_binary64_1173` `sqrt-pow1_binary64_1119` `div-exp_binary64_1152` `pow1/2_binary64_1181`

Counts

4 → 187

Calls

8 calls:

14.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)))
12.0ms	(pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

series357.0ms (0.5%)

Counts

4 → 21

Calls

4 calls:

270.0ms	(pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)
49.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3) 3)))
24.0ms	(sqrt.f64 (cos.f64 x))
15.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 548 to 388 computations (29.2% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5345	5852

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

3.6b	(fmod.f64 (exp.f64 x) 1)
3.6b	(fmod.f64 (exp.f64 x) 1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`

Counts

1 → 7

Calls

2 calls:

0.0ms	(fmod.f64 (exp.f64 x) 1)
0.0ms	(fmod.f64 (exp.f64 x) 1)

series8.0ms (0%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(fmod.f64 (exp.f64 x) 1)

Compiler

Compiled 24 to 24 computations (0% saved)

simplify151.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	4715	85
1	4715	85

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3)
0.0b	(+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x))
0.0b	(.f64 (.f64 x x) 1/4)
0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3))
0.1b	(*.f64 1/96 (pow.f64 x 4))
3.6b	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_1123`
37×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
36×	`times-frac_binary64_1107`
32×	`cbrt-prod_binary64_1132`
30×	`unpow-prod-down_binary64_1180`
26×	`cube-prod_binary64_1129`
11×	`add-exp-log_binary64_1139`
9×	`add-cbrt-cube_binary64_1137`
7×	`associate-r_binary64_1041`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `sqr-pow_binary64_1073`
3×	`pow-exp_binary64_1169` `prod-exp_binary64_1150` `pow-unpow_binary64_1178` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
2×	`cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `cube-div_binary64_1130` `unpow3_binary64_1167` `pow-to-exp_binary64_1170`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `pow1/3_binary64_1183` `pow-pow_binary64_1173` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-div_binary64_1133` `rem-cbrt-cube_binary64_1125`

Counts

4 → 120

Calls

8 calls:

6.0ms	(*.f64 1/96 (pow.f64 x 4))
6.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3))
6.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3)
1.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))
0.0ms	(.f64 (.f64 x x) 1/4)

series381.0ms (0.5%)

Counts

4 → 18

Calls

4 calls:

244.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3)
82.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))) (exp.f64 x)) 3))
30.0ms	(*.f64 1/96 (pow.f64 x 4))
24.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))

Compiler

Compiled 846 to 684 computations (19.1% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5332	5004

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (sqrt.f64 (cos.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
0.0b	(exp.f64 (sqrt.f64 (cos.f64 x)))
0.1b	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
2.5b	(log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
3.6b	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`exp-prod_binary64_1153`
15×	`log-pow_binary64_1190`
13×	`log-prod_binary64_1187`
12×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`sqrt-prod_binary64_1117`
7×	`pow1_binary64_1162`
5×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139`
4×	`add-cbrt-cube_binary64_1137`
2×	`rem-log-exp_binary64_1142`
1×	`rem-exp-log_binary64_1141`

Counts

4 → 58

Calls

8 calls:

3.0ms	(log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
3.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
3.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
1.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

series310.0ms (0.4%)

Counts

4 → 21

Calls

4 calls:

176.0ms	(log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
85.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
30.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
19.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

Compiler

Compiled 481 to 375 computations (22% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5101	888

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))
0.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x)))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))))
0.0b	(cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x)))
3.6b	(fmod.f64 (exp.f64 x) 1)
3.6b	(fmod.f64 (exp.f64 x) 1)
3.6b	(fmod.f64 (exp.f64 x) 1)

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`cbrt-prod_binary64_1132`
11×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
1×	`pow1/3_binary64_1183` `div-inv_binary64_1098` `cbrt-div_binary64_1133`

Counts

4 → 43

Calls

8 calls:

5.0ms	(cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x)))
1.0ms	(fmod.f64 (exp.f64 x) 1)
1.0ms	(fmod.f64 (exp.f64 x) 1)
1.0ms	(fmod.f64 (exp.f64 x) 1)
0.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x)))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x))))

series179.0ms (0.2%)

Counts

4 → 15

Calls

4 calls:

143.0ms	(cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) 1) (exp.f64 x)))
12.0ms	(fmod.f64 (exp.f64 x) 1)
12.0ms	(fmod.f64 (exp.f64 x) 1)
11.0ms	(fmod.f64 (exp.f64 x) 1)

Compiler

Compiled 744 to 474 computations (36.3% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4904	842
1	4904	842

prune12.6s (16.8%)

Pruning

334 alts after pruning (323 fresh and 11 done)

	Pruned	Kept	Total
New	344	149	493
Fresh	20	174	194
Picked	0	0	0
Done	1	11	12
Total	365	334	699

Error

19.6b

Counts

699 → 334

Compiler

Compiled 14648 to 9077 computations (38% saved)

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))))
0.0b	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))
1.3b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
1.3b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
46.5b	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))))
47.8b	(log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`pow1_binary64_1162`
18×	`log-prod_binary64_1187`
16×	`log-pow_binary64_1190`
11×	`pow1/3_binary64_1183`
9×	`pow-prod-up_binary64_1171`
7×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
6×	`pow-plus_binary64_1164` `cbrt-prod_binary64_1132`
5×	`add-exp-log_binary64_1139` `pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`pow-sqr_binary64_1074`
2×	`pow2_binary64_1182`
1×	`rem-log-exp_binary64_1142` `pow3_binary64_1184`

Counts

4 → 56

Calls

8 calls:

12.0ms	(log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))
3.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
3.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
1.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))))
0.0ms	(/.f64 (fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))

series469.0ms (0.6%)

Counts

4 → 21

Calls

4 calls:

174.0ms	(log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))
139.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
127.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
28.0ms	(fmod.f64 (exp.f64 x) (exp.f64 (log.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))))

Compiler

Compiled 725 to 505 computations (30.3% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1002
1	4899	1002

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

3.6b	(fmod.f64 (exp.f64 x) 1)
3.6b	(fmod.f64 (exp.f64 x) 1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`

Counts

1 → 7

Calls

2 calls:

1.0ms	(fmod.f64 (exp.f64 x) 1)
0.0ms	(fmod.f64 (exp.f64 x) 1)

series9.0ms (0%)

Counts

1 → 3

Calls

1 calls:

9.0ms

(fmod.f64 (exp.f64 x) 1)

Compiler

Compiled 36 to 36 computations (0% saved)

simplify154.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4715	85
1	4715	85

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
0.0b	(exp.f64 (sqrt.f64 (cos.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(*.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 (neg.f64 x)))
0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(exp.f64 (sqrt.f64 (cos.f64 x)))
0.1b	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
3.6b	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`exp-prod_binary64_1153`
11×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`sqrt-prod_binary64_1117`
7×	`log-pow_binary64_1190`
6×	`pow1_binary64_1162`
5×	`add-log-exp_binary64_1140`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`log-prod_binary64_1187`
1×	`rem-sqrt-square_binary64_1114` `rem-exp-log_binary64_1141` `rem-log-exp_binary64_1142` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`

Counts

4 → 52

Calls

8 calls:

3.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
0.0ms	(*.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 (neg.f64 x)))

series157.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

85.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
31.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
25.0ms	(sqrt.f64 (cos.f64 x))
17.0ms	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

Compiler

Compiled 444 to 372 computations (16.2% saved)

simplify104.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4931	722
1	4931	722

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x))))) (cbrt.f64 (exp.f64 (neg.f64 x))))
0.0b	(cbrt.f64 (exp.f64 (neg.f64 x)))
0.0b	(cbrt.f64 (exp.f64 (neg.f64 x)))
0.0b	(cbrt.f64 (exp.f64 (neg.f64 x)))
0.0b	(*.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x))))
0.0b	(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x)))))
0.0b	(sqrt.f64 (cos.f64 x))
3.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1123` `cbrt-div_binary64_1133`
17×	`pow1_binary64_1162`
16×	`cbrt-prod_binary64_1132`
14×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
12×	`exp-diff_binary64_1149` `neg-sub0_binary64_1096` `associate-*r/_binary64_1043` `exp-neg_binary64_1148`
11×	`add-exp-log_binary64_1139`
9×	`associate-l_binary64_1042`
8×	`frac-times_binary64_1111`
7×	`add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
6×	`pow1/3_binary64_1183` `swap-sqr_binary64_1068`
5×	`pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `associate-*l/_binary64_1044`
3×	`sqrt-prod_binary64_1117`
2×	`*-commutative_binary64_1032` `pow-prod-up_binary64_1171` `pow-sqr_binary64_1074`
1×	`pow-plus_binary64_1164` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow2_binary64_1182` `pow1/2_binary64_1181`

Counts

4 → 95

Calls

8 calls:

10.0ms	(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x)))))
9.0ms	(*.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x))))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
0.0ms	(cbrt.f64 (exp.f64 (neg.f64 x)))

series258.0ms (0.3%)

Counts

4 → 21

Calls

4 calls:

120.0ms	(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x)))))
94.0ms	(*.f64 (cbrt.f64 (exp.f64 (neg.f64 x))) (cbrt.f64 (exp.f64 (neg.f64 x))))
29.0ms	(sqrt.f64 (cos.f64 x))
15.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 676 to 438 computations (35.2% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5157	1702

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))))
0.0b	(sqrt.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4))))))
0.0b	(.f64 (.f64 x x) 1/4)
0.0b	(.f64 (.f64 x x) 1/4)
0.1b	(*.f64 1/96 (pow.f64 x 4))
0.3b	(/.f64 (pow.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))) 3) (exp.f64 (+.f64 x x)))
3.6b	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))
3.6b	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))

rewrite47.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`times-frac_binary64_1107`
56×	`add-sqr-sqrt_binary64_1123`
51×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
34×	`unpow-prod-down_binary64_1180`
30×	`cube-prod_binary64_1129` `sqrt-prod_binary64_1117`
19×	`exp-sum_binary64_1147`
18×	`associate-/l*_binary64_1046`
11×	`add-exp-log_binary64_1139`
8×	`add-cbrt-cube_binary64_1137`
7×	`associate-r_binary64_1041` `sqr-pow_binary64_1073`
5×	`cube-mult_binary64_1131` `unpow3_binary64_1167`
4×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `associate-/r*_binary64_1045`
3×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
2×	`pow-exp_binary64_1169` `pow-to-exp_binary64_1170`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `cbrt-undiv_binary64_1135`

Counts

4 → 147

Calls

8 calls:

13.0ms	(/.f64 (pow.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))) 3) (exp.f64 (+.f64 x x)))
6.0ms	(*.f64 1/96 (pow.f64 x 4))
1.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))
1.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))
0.0ms	(.f64 (.f64 x x) 1/4)

series381.0ms (0.5%)

Counts

4 → 15

Calls

4 calls:

275.0ms	(/.f64 (pow.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))) 3) (exp.f64 (+.f64 x x)))
39.0ms	(*.f64 1/96 (pow.f64 x 4))
36.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))
30.0ms	(fmod.f64 (exp.f64 x) (-.f64 1 (+.f64 (.f64 (.f64 x x) 1/4) (*.f64 1/96 (pow.f64 x 4)))))

Compiler

Compiled 1386 to 1070 computations (22.8% saved)

simplify111.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4962	7088
1	4962	7088

prune18.9s (25.1%)

Pruning

473 alts after pruning (457 fresh and 16 done)

	Pruned	Kept	Total
New	290	148	438
Fresh	9	309	318
Picked	0	0	0
Done	0	16	16
Total	299	473	772

Error

19.6b

Counts

772 → 473

Compiler

Compiled 9364 to 4600 computations (50.9% saved)

simplify578.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4680	34125
1	4680	34125

regimes3.4s (4.6%)

Compiler: Compiled 34184 to 23362 computations (31.7% saved)

bsearch119.0ms (0.2%)

Steps

Iters	Range		Point
9	-1.111492366929206e-308	1.0127861305179967e-303	2.6134317790376e-310

Compiler

Compiled 1 to 1 computations (0% saved)

regimes1.5s (2%)

Compiler: Compiled 13110 to 9844 computations (24.9% saved)

bsearch173.0ms (0.2%)

Steps

Iters	Range		Point
9	0.8920752688190553	879631000.6661552	163559103.077314
9	-1.111492366929206e-308	1.0127861305179967e-303	2.6134317790376e-310

Compiler

Compiled 1 to 1 computations (0% saved)

regimes704.0ms (0.9%)

Compiler: Compiled 5590 to 4352 computations (22.1% saved)

bsearch168.0ms (0.2%)

Steps

Iters	Range		Point
9	0.8920752688190553	879631000.6661552	163559103.077314
9	-1.111492366929206e-308	1.0127861305179967e-303	2.6134317790376e-310

Compiler

Compiled 1 to 1 computations (0% saved)

regimes690.0ms (0.9%)

Compiler: Compiled 5426 to 4228 computations (22.1% saved)

bsearch167.0ms (0.2%)

Steps

Iters	Range		Point
9	0.8920752688190553	879631000.6661552	163559103.077314
9	-1.111492366929206e-308	1.0127861305179967e-303	2.6134317790376e-310

Compiler

Compiled 1 to 1 computations (0% saved)

regimes81.0ms (0.1%)

Accuracy

Total 0.5b remaining (2.2%)

Threshold costs 0.5b (2.2%)

Compiler

Compiled 408 to 328 computations (19.6% saved)

bsearch91.0ms (0.1%)

Steps

Iters	Range		Point
9	-1.111492366929206e-308	1.0127861305179967e-303	2.6134317790376e-310

Compiler

Compiled 98 to 80 computations (18.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	152
1	52	152

end0.0ms (0%)

sample21.6s (28.8%)

Algorithm

1×

intervals

Results

2.8s	1584×	body	8192	exit
1.6s	3989×	body	1024	valid
693.0ms	1625×	body	1024	nan
477.0ms	2013×	body	512	valid
150.0ms	803×	body	512	nan
145.0ms	966×	body	256	valid
101.0ms	157×	body	2048	valid
76.0ms	875×	body	128	valid
60.0ms	383×	body	256	nan
31.0ms	418×	body	128	nan
0.0ms	1×	body	2048	nan

Compiler

Compiled 17270 to 11826 computations (31.5% saved)

Pareto

0.9741267087690715