Details

analyze1.1s (9.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Compiler

Compiled 20 to 20 computations (0% saved)

sample76.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	45×	body	1024	valid
13.0ms	27×	body	2048	valid
13.0ms	157×	body	128	valid
6.0ms	80×	body	128	nan
5.0ms	21×	body	512	valid
3.0ms	33×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify140.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

20.6b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(/.f64 a (*.f64 b 3))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
24.1b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64_19210` `add-exp-log_binary64_19212`
11×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209` `add-sqr-sqrt_binary64_19196`
9×	`pow1_binary64_19235` `times-frac_binary64_19180`
8×	`cos-sum_binary64_19308`
7×	`cancel-sign-sub-inv_binary64_19140`
5×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207`
4×	`associate-/l_binary64_19119` `add-log-exp_binary64_19213` `associate-/r_binary64_19118` `div-exp_binary64_19225` `cbrt-undiv_binary64_19208`
3×	`div-inv_binary64_19171` `associate-r_binary64_19114` `pow-prod-down_binary64_19245` `cos-diff_binary64_19311`
2×	`frac-2neg_binary64_19185` `clear-num_binary64_19173`
1×	`distribute-lft-in_binary64_19123` `-commutative_binary64_19105` `associate-l*_binary64_19115` `sub-neg_binary64_19167` `distribute-rgt-in_binary64_19124`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
8.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
4.0ms	(/.f64 (*.f64 z t) 3)
4.0ms	(/.f64 a (*.f64 b 3))

series192.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
41.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
15.0ms	(/.f64 (*.f64 z t) 3)
13.0ms	(/.f64 a (*.f64 b 3))

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4928	1387
1	4928	1387

prune170.0ms (1.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	71	19	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	19	91

Error

16.2b

Counts

91 → 19

Compiler

Compiled 2648 to 1762 computations (33.5% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (/.f64 (.f64 z t) 3))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (*.f64 t -1/3))))))
0.3b	(*.f64 t -1/3)
30.0b	(cos.f64 (/.f64 (*.f64 z t) 3))
30.0b	(sin.f64 (.f64 z (.f64 t -1/3)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_19210` `pow1_binary64_19235` `add-exp-log_binary64_19212`
9×	`add-sqr-sqrt_binary64_19196`
7×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
6×	`associate-r_binary64_19114`
4×	`prod-exp_binary64_19223` `associate-r/_binary64_19116` `add-log-exp_binary64_19213` `cbrt-unprod_binary64_19207` `pow-prod-down_binary64_19245` `associate-l*_binary64_19115`
2×	`distribute-lft-in_binary64_19123` `*-commutative_binary64_19105` `sub-neg_binary64_19167` `distribute-rgt-in_binary64_19124` `sin-mult_binary64_19329` `cancel-sign-sub-inv_binary64_19140` `cos-mult_binary64_19328`
1×	`flip--_binary64_19149` `flip3--_binary64_19178` `frac-sub_binary64_19183` `unswap-sqr_binary64_19142` `sub-div_binary64_19181`

Counts

4 → 58

Calls

4 calls:

12.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (/.f64 (.f64 z t) 3))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (*.f64 t -1/3))))))
4.0ms	(*.f64 t -1/3)
2.0ms	(sin.f64 (.f64 z (.f64 t -1/3)))
2.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))

series303.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (-.f64 (.f64 (cos.f64 y) (cos.f64 (/.f64 (.f64 z t) 3))) (.f64 (sin.f64 y) (sin.f64 (.f64 z (*.f64 t -1/3))))))
14.0ms	(sin.f64 (.f64 z (.f64 t -1/3)))
11.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))
10.0ms	(*.f64 t -1/3)

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4926	1677
1	4926	1677

prune178.0ms (1.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	5	13	18
Picked	1	0	1
Done	0	0	0
Total	66	23	89

Error

16.0b

Counts

89 → 23

Compiler

Compiled 3372 to 2215 computations (34.3% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
1.0b	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
30.0b	(cos.f64 (/.f64 (*.f64 z t) 3))
30.1b	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_19196`
20×	`pow1_binary64_19235`
19×	`cbrt-prod_binary64_19205`
15×	`add-exp-log_binary64_19212`
14×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
12×	`associate-r_binary64_19114`
8×	`pow-prod-down_binary64_19245` `add-cbrt-cube_binary64_19210`
7×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207` `associate-l_binary64_19115`
6×	`swap-sqr_binary64_19141` `pow1/3_binary64_19256`
4×	`add-log-exp_binary64_19213` `unswap-sqr_binary64_19142`
2×	`pow-sqr_binary64_19147` `*-commutative_binary64_19105` `pow-prod-up_binary64_19244`
1×	`pow2_binary64_19255` `pow-plus_binary64_19237`

Counts

4 → 78

Calls

4 calls:

11.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
6.0ms	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
4.0ms	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))
2.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))

series114.0ms (1%)

Counts

4 → 10

Calls

4 calls:

57.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
47.0ms	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))
10.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))
0.0ms	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5267	758

prune222.0ms (2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	21	22
Picked	1	0	1
Done	0	0	0
Total	85	26	111

Error

15.9b

Counts

111 → 26

Compiler

Compiled 4219 to 2952 computations (30% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
1.0b	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
30.0b	(cos.f64 (/.f64 (*.f64 z t) 3))
30.1b	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_19196`
20×	`pow1_binary64_19235`
19×	`cbrt-prod_binary64_19205`
15×	`add-exp-log_binary64_19212`
14×	`*-un-lft-identity_binary64_19174` `add-cube-cbrt_binary64_19209`
12×	`associate-r_binary64_19114`
8×	`pow-prod-down_binary64_19245` `add-cbrt-cube_binary64_19210`
7×	`prod-exp_binary64_19223` `cbrt-unprod_binary64_19207` `associate-l_binary64_19115`
6×	`swap-sqr_binary64_19141` `pow1/3_binary64_19256`
4×	`add-log-exp_binary64_19213` `unswap-sqr_binary64_19142`
2×	`pow-sqr_binary64_19147` `*-commutative_binary64_19105` `pow-prod-up_binary64_19244`
1×	`pow2_binary64_19255` `pow-plus_binary64_19237`

Counts

4 → 78

Calls

4 calls:

12.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
7.0ms	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))
4.0ms	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))
2.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))

series114.0ms (1%)

Counts

4 → 10

Calls

4 calls:

61.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))
43.0ms	(sin.f64 (.f64 z (.f64 (.f64 t (.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))) (cbrt.f64 -1/3))))
10.0ms	(cos.f64 (/.f64 (*.f64 z t) 3))
0.0ms	(*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5267	758

prune178.0ms (1.6%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	89	25	114

Error

15.9b

Counts

114 → 25

Compiler

Compiled 3489 to 2340 computations (32.9% saved)

regimes3.5s (31.2%)

Accuracy

Total 1.5b remaining (8.5%)

Threshold costs 0b (0%)

Compiler

Compiled 39273 to 35069 computations (10.7% saved)

bsearch5.0ms (0%)

Compiler: Compiled 13 to 15 computations (-15.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	164	116
1	164	116

end0.0ms (0%)

sample4.3s (39.1%)

Algorithm

1×

intervals

Results

546.0ms	1637×	body	1024	valid
355.0ms	4586×	body	128	valid
351.0ms	757×	body	2048	valid
196.0ms	2394×	body	128	nan
175.0ms	704×	body	512	valid
93.0ms	1140×	body	128	invalid
52.0ms	315×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 2416 to 2134 computations (11.7% saved)

Details

analyze1.1s (9.6%)

sample76.0ms (0.7%)

simplify140.0ms (1.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite36.0ms (0.3%)

series192.0ms (1.7%)

simplify67.0ms (0.6%)

prune170.0ms (1.5%)

localize27.0ms (0.2%)

rewrite26.0ms (0.2%)

series303.0ms (2.7%)

simplify94.0ms (0.9%)

prune178.0ms (1.6%)

localize28.0ms (0.3%)

rewrite35.0ms (0.3%)

series114.0ms (1%)

simplify58.0ms (0.5%)

prune222.0ms (2%)

localize37.0ms (0.3%)

rewrite34.0ms (0.3%)

series114.0ms (1%)

simplify57.0ms (0.5%)

prune178.0ms (1.6%)

regimes3.5s (31.2%)

bsearch5.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.3s (39.1%)

Profiling