Details

analyze344.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample88.0ms (1.7%)

Algorithm

1×

intervals

Results

36.0ms	81×	body	1024	valid
14.0ms	50×	body	1024	invalid
9.0ms	130×	body	128	valid
6.0ms	27×	body	512	valid
5.0ms	70×	body	128	invalid
3.0ms	15×	body	512	invalid
2.0ms	18×	body	256	valid
1.0ms	11×	body	256	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify250.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5100	18

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `*-un-lft-identity_binary64_77`
4×	`add-log-exp_binary64_113` `associate-r_binary64_19`
3×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `associate-*r/_binary64_21` `distribute-lft-out_binary64_30`
1×	`associate-l_binary64_20` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `*-commutative_binary64_10` `distribute-rgt-in_binary64_29` `sum-log_binary64_165`

Counts

2 → 35

Calls

2 calls:

12.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series160.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

134.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
26.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4885	719
1	4885	719

prune43.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	36	5	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	5	42

Merged error: 0.0b

Counts

42 → 5

Compiler

Compiled 737 to 312 computations (57.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(*.f64 (sin.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64_77`
6×	`add-sqr-sqrt_binary64_98`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `associate-r_binary64_19`
3×	`associate-l_binary64_20`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `associate-*r/_binary64_21` `distribute-lft-out_binary64_30`
1×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `distribute-rgt-in_binary64_29` `sum-log_binary64_165`

Counts

2 → 35

Calls

2 calls:

10.0ms	(*.f64 (sin.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series136.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

110.0ms	(*.f64 (sin.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
26.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4876	661
1	4876	661

prune35.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	42	4	46

Merged error: 0.0b

Counts

46 → 4

Compiler

Compiled 738 to 269 computations (63.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3))
0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
0.0b	(pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_105` `*-un-lft-identity_binary64_77`
17×	`associate-r_binary64_19`
14×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
12×	`unpow-prod-down_binary64_153` `cube-prod_binary64_102`
10×	`add-exp-log_binary64_112` `pow1_binary64_135`
8×	`add-cbrt-cube_binary64_110`
7×	`distribute-lft-out_binary64_30`
6×	`add-log-exp_binary64_113` `cube-div_binary64_103`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `cbrt-div_binary64_106`
3×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `sqr-pow_binary64_49` `cube-mult_binary64_104` `pow-unpow_binary64_151` `prod-exp_binary64_123` `unpow3_binary64_140`
2×	`associate-*r/_binary64_21`
1×	`pow-to-exp_binary64_143` `rem-cbrt-cube_binary64_100` `rem-cube-cbrt_binary64_99` `associate-l_binary64_20` `pow-exp_binary64_142` `+-commutative_binary64_9` `*-commutative_binary64_10` `pow1/3_binary64_156` `pow-pow_binary64_146` `sum-log_binary64_165`

Counts

4 → 98

Calls

4 calls:

15.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
8.0ms	(pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)
8.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3))
6.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series261.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)))
87.0ms	(pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3)
27.0ms	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
26.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) 3))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5246	1877

prune105.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0b

Counts

114 → 4

Compiler

Compiled 2113 to 917 computations (56.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (sin.f64 re) (exp.f64 im)) (*.f64 (sin.f64 re) (exp.f64 im)))
0.0b	(*.f64 (sin.f64 re) (exp.f64 im))
0.0b	(/.f64 (sin.f64 re) (exp.f64 im))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_98`
13×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
9×	`times-frac_binary64_83`
7×	`add-cbrt-cube_binary64_110`
5×	`add-exp-log_binary64_112` `add-log-exp_binary64_113` `pow1_binary64_135`
3×	`associate-/r_binary64_23` `associate-l_binary64_20` `associate-/l_binary64_24` `associate-r_binary64_19`
2×	`div-inv_binary64_74`
1×	`pow-prod-down_binary64_145` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `+-commutative_binary64_9` `div-exp_binary64_125` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `clear-num_binary64_76` `frac-2neg_binary64_88` `distribute-lft-out_binary64_30` `sum-log_binary64_165`

Counts

3 → 57

Calls

3 calls:

9.0ms	(+.f64 (/.f64 (sin.f64 re) (exp.f64 im)) (*.f64 (sin.f64 re) (exp.f64 im)))
6.0ms	(*.f64 (sin.f64 re) (exp.f64 im))
5.0ms	(/.f64 (sin.f64 re) (exp.f64 im))

series253.0ms (5%)

Counts

3 → 9

Calls

3 calls:

127.0ms	(+.f64 (/.f64 (sin.f64 re) (exp.f64 im)) (*.f64 (sin.f64 re) (exp.f64 im)))
72.0ms	(/.f64 (sin.f64 re) (exp.f64 im))
53.0ms	(*.f64 (sin.f64 re) (exp.f64 im))

simplify95.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4883	956
1	4883	956

prune51.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	67	3	70

Merged error: 0b

Counts

70 → 3

Compiler

Compiled 1181 to 356 computations (69.9% saved)

regimes44.0ms (0.9%)

Compiler: Compiled 192 to 168 computations (12.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	13	21

end0.0ms (0%)

sample2.9s (56.2%)

Algorithm

1×

intervals

Results

904.0ms	2046×	body	1024	valid
552.0ms	1926×	body	1024	invalid
298.0ms	4433×	body	128	valid
217.0ms	982×	body	512	valid
171.0ms	916×	body	512	invalid
167.0ms	2562×	body	128	invalid
75.0ms	535×	body	256	valid
65.0ms	471×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 70 to 59 computations (15.7% saved)

Details

analyze344.0ms (6.7%)

sample88.0ms (1.7%)

simplify250.0ms (4.9%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite20.0ms (0.4%)

series160.0ms (3.1%)

simplify73.0ms (1.4%)

prune43.0ms (0.8%)

localize10.0ms (0.2%)

rewrite19.0ms (0.4%)

series136.0ms (2.7%)

simplify69.0ms (1.4%)

prune35.0ms (0.7%)

localize15.0ms (0.3%)

rewrite45.0ms (0.9%)

series261.0ms (5.1%)

simplify66.0ms (1.3%)

prune105.0ms (2.1%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series253.0ms (5%)

simplify95.0ms (1.9%)

prune51.0ms (1%)

regimes44.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (56.2%)

Profiling