Details

analyze949.0ms (8%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample61.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	188×	body	128	valid
10.0ms	31×	body	1024	valid
9.0ms	24×	body	512	valid
5.0ms	67×	body	128	invalid
2.0ms	7×	body	1024	invalid
2.0ms	13×	body	256	valid
2.0ms	8×	body	512	invalid
1.0ms	6×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify262.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	7278	24

prune5.0ms (0%)

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

Error

28.2b

Counts

2 → 1

Compiler

Compiled 32 to 24 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

16.8b	(.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s))))
9.4b	(.f64 x (.f64 s s))
4.6b	(.f64 x (.f64 x (*.f64 s s)))
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
4.6b	(.f64 x (.f64 x (*.f64 s s)))
9.4b	(.f64 x (.f64 s s))
16.8b	(.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s))))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
57×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
50×	`pow1_binary64_480`
33×	`pow-prod-down_binary64_490`
9×	`add-sqr-sqrt_binary64_441` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
7×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458`
3×	`times-frac_binary64_425` `associate-r_binary64_359` `-commutative_binary64_350` `associate-/l_binary64_364`
1×	`cos-2_binary64_561` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `associate-/r*_binary64_363` `div-sub_binary64_424`

Counts

4 → 110

Calls

8 calls:

15.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
14.0ms	(.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s))))
11.0ms	(.f64 x (.f64 x (*.f64 s s)))
6.0ms	(.f64 x (.f64 s s))
0.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))

series686.0ms (5.8%)

Counts

4 → 33

Calls

4 calls:

371.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 x (.f64 x (.f64 s s)))))
181.0ms	(.f64 (.f64 c c) (.f64 x (.f64 x (*.f64 s s))))
74.0ms	(.f64 x (.f64 x (*.f64 s s)))
59.0ms	(.f64 x (.f64 s s))

Compiler

Compiled 1058 to 949 computations (10.3% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4987	2539
1	4987	2539

prune177.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	132	11	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Error

13.5b

Counts

144 → 11

Compiler

Compiled 2953 to 1262 computations (57.3% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

16.8b	(.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s))))
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (.f64 x s)))))
0.2b	(.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s)))
0.2b	(.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s)))
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (.f64 x s)))))
16.8b	(.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s))))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`pow1_binary64_480`
35×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
17×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
15×	`pow-prod-down_binary64_490`
11×	`add-sqr-sqrt_binary64_441`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
5×	`pow-plus_binary64_482` `pow-prod-up_binary64_489` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`associate-r_binary64_359` `associate-l_binary64_360`
3×	`times-frac_binary64_425` `add-log-exp_binary64_458` `swap-sqr_binary64_386` `pow-sqr_binary64_392` `pow2_binary64_500` `associate-/l*_binary64_364`
2×	`unswap-sqr_binary64_387` `*-commutative_binary64_350`
1×	`cos-2_binary64_561` `clear-num_binary64_418` `div-inv_binary64_416` `sqr-abs_binary64_434` `frac-2neg_binary64_430` `associate-/r*_binary64_363` `div-sub_binary64_424`

Counts

3 → 83

Calls

6 calls:

14.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (.f64 x s)))))
9.0ms	(.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s))))
4.0ms	(.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s)))
0.0ms	(.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (*.f64 x s)))
0.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 c c) (.f64 (fabs.f64 (.f64 x s)) (fabs.f64 (.f64 x s)))))

series654.0ms (5.5%)

Counts

3 → 27

Calls

3 calls:

442.0ms

(/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (*.f64 c c) (*.f64 (fabs.f64 (*.f64 x s)) (fabs.f64 (*.f64 x s)))))

161.0ms

(*.f64 (*.f64 c c) (*.f64 (fabs.f64 (*.f64 x s)) (fabs.f64 (*.f64 x s))))

50.0ms

(*.f64 (fabs.f64 (*.f64 x s)) (fabs.f64 (*.f64 x s)))

Compiler

Compiled 840 to 746 computations (11.2% saved)

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4962	1908
1	4962	1908

prune154.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Error

1.7b

Counts

121 → 14

Compiler

Compiled 2332 to 1175 computations (49.6% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

3.4b	(.f64 c (fabs.f64 (.f64 x s)))
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 x s))) 2))
0.3b	(pow.f64 (.f64 c (fabs.f64 (.f64 x s))) 2)
0.3b	(pow.f64 (.f64 c (fabs.f64 (.f64 x s))) 2)
0.9b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 x s))) 2))
3.4b	(.f64 c (fabs.f64 (.f64 x s)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_441`
18×	`times-frac_binary64_425`
17×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
16×	`add-exp-log_binary64_457`
8×	`pow1_binary64_480`
7×	`add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`unpow-prod-down_binary64_498` `sqr-pow_binary64_391` `unpow2_binary64_484`
4×	`pow-exp_binary64_487` `div-exp_binary64_470`
3×	`add-log-exp_binary64_458` `associate-r_binary64_359` `prod-exp_binary64_468` `associate-l_binary64_360` `pow-unpow_binary64_496` `associate-/l*_binary64_364`
2×	`pow-prod-down_binary64_490` `pow-to-exp_binary64_488` `pow-pow_binary64_491`
1×	`cos-2_binary64_561` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `frac-2neg_binary64_430` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

3 → 79

Calls

6 calls:

5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 x s))) 2))
4.0ms	(.f64 c (fabs.f64 (.f64 x s)))
4.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 x s))) 2)
0.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 x s))) 2)
0.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 x s))) 2))

series638.0ms (5.4%)

Counts

3 → 30

Calls

3 calls:

448.0ms	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (.f64 c (fabs.f64 (*.f64 x s))) 2))
120.0ms	(pow.f64 (.f64 c (fabs.f64 (.f64 x s))) 2)
70.0ms	(.f64 c (fabs.f64 (.f64 x s)))

Compiler

Compiled 894 to 806 computations (9.8% saved)

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5854	2249

prune183.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Error

1.5b

Counts

123 → 15

Compiler

Compiled 2422 to 1263 computations (47.9% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (*.f64 x 2)))
0.5b	(cbrt.f64 (cos.f64 (*.f64 x 2)))
0.3b	(.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (*.f64 x 2))))
0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (.f64 x 2)))) (.f64 c (fabs.f64 (.f64 x s)))) (/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (.f64 c (fabs.f64 (*.f64 x s)))))
0.9b	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (.f64 c (fabs.f64 (*.f64 x s))))
0.9b	(/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (.f64 x 2)))) (.f64 c (fabs.f64 (*.f64 x s))))
3.4b	(.f64 c (fabs.f64 (.f64 x s)))
3.4b	(.f64 c (fabs.f64 (.f64 x s)))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_457`
19×	`add-cbrt-cube_binary64_455`
16×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`pow1_binary64_480`
7×	`times-frac_binary64_425` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/l*_binary64_364`
6×	`associate-r_binary64_359` `cbrt-prod_binary64_450` `associate-l_binary64_360` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458`
2×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/r_binary64_363`

Counts

4 → 84

Calls

8 calls:

9.0ms	(/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (.f64 x 2)))) (.f64 c (fabs.f64 (*.f64 x s))))
5.0ms	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (.f64 c (fabs.f64 (*.f64 x s))))
4.0ms	(.f64 c (fabs.f64 (.f64 x s)))
4.0ms	(.f64 c (fabs.f64 (.f64 x s)))
0.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (.f64 x 2)))) (.f64 c (fabs.f64 (.f64 x s)))) (/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (.f64 c (fabs.f64 (*.f64 x s)))))

series1.3s (11.2%)

Counts

4 → 42

Calls

4 calls:

636.0ms	(/.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (cbrt.f64 (cos.f64 (.f64 x 2)))) (.f64 c (fabs.f64 (*.f64 x s))))
520.0ms	(/.f64 (cbrt.f64 (cos.f64 (.f64 x 2))) (.f64 c (fabs.f64 (*.f64 x s))))
84.0ms	(.f64 c (fabs.f64 (.f64 x s)))
83.0ms	(.f64 c (fabs.f64 (.f64 x s)))

Compiler

Compiled 2488 to 1976 computations (20.6% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5012	2322

prune310.0ms (2.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	124	17	141

Error

1.5b

Counts

141 → 17

Compiler

Compiled 4309 to 2202 computations (48.9% saved)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	431	2503
1	431	2503

regimes748.0ms (6.3%)

Compiler: Compiled 7963 to 5745 computations (27.9% saved)

bsearch0.0ms (0%)

regimes416.0ms (3.5%)

Compiler: Compiled 1788 to 1535 computations (14.1% saved)

bsearch0.0ms (0%)

regimes83.0ms (0.7%)

Compiler: Compiled 705 to 579 computations (17.9% saved)

bsearch0.0ms (0%)

regimes141.0ms (1.2%)

Compiler: Compiled 537 to 426 computations (20.7% saved)

bsearch185.0ms (1.6%)

Steps

Iters	Range		Point
10	1.1975609624569152e+83	2.0549697430387255e+93	2.0376561209920545e+93
10	1.0994781813968999e-155	2.727155300585716e-138	5.632597730250348e-147
8	-3.307468919280227e-155	-1.717334986939566e-159	-1.9446361780504217e-157
7	-1.5181119040468767e+103	-4.5058310705676076e+101	-8.065984647911511e+102

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes93.0ms (0.8%)

Compiler: Compiled 507 to 396 computations (21.9% saved)

bsearch126.0ms (1.1%)

Steps

Iters	Range		Point
12	4.990884062215047e-252	2.2209248347615567e-187	2.1907951057584004e-187
5	-2.4813775017622595e-136	-8.3856812216306435e-137	-9.977162136642538e-137

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes68.0ms (0.6%)

Compiler: Compiled 309 to 249 computations (19.4% saved)

bsearch130.0ms (1.1%)

Steps

Iters	Range		Point
9	1.1662561528480583e-163	6.049547216295386e-155	1.5984194736341986e-162
11	-5.241141468785823e-128	-2.1653305446420412e-150	-2.1875156225120967e-150

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes66.0ms (0.6%)

Compiler: Compiled 261 to 213 computations (18.4% saved)

bsearch139.0ms (1.2%)

Steps

Iters	Range		Point
9	1.1662561528480583e-163	6.049547216295386e-155	1.5984194736341986e-162
11	-5.241141468785823e-128	-2.1653305446420412e-150	-2.1875156225120967e-150

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes63.0ms (0.5%)

Compiler: Compiled 213 to 177 computations (16.9% saved)

bsearch136.0ms (1.1%)

Steps

Iters	Range		Point
9	1.1662561528480583e-163	6.049547216295386e-155	1.5984194736341986e-162
11	-5.241141468785823e-128	-2.1653305446420412e-150	-2.1875156225120967e-150

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes63.0ms (0.5%)

Compiler: Compiled 165 to 141 computations (14.5% saved)

bsearch37.0ms (0.3%)

Steps

Iters	Range		Point
10	7.561967265424339e+26	8.382443517477107e+36	7.662776146193135e+26
0	-0.014993039030358613	-0.014842262609760605	-0.01491765082005961

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes56.0ms (0.5%)

Compiler: Compiled 54 to 84 computations (-55.6% saved)

bsearch25.0ms (0.2%)

Steps

Iters	Range		Point
6	1.946632989001461e+109	1.4507705344406814e+110	2.3289896555315027e+109
0	-0.014993039030358613	-0.014842262609760605	-0.01491765082005961

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes25.0ms (0.2%)

Accuracy

Total 0.4b remaining (16.6%)

Threshold costs 0.4b (16.6%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch15.0ms (0.1%)

Compiler: Compiled 375 to 232 computations (38.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	135	443
1	135	443

end0.0ms (0%)

sample3.3s (27.6%)

Algorithm

1×

intervals

Results

500.0ms	6067×	body	128	valid
341.0ms	1021×	body	1024	valid
157.0ms	1850×	body	128	invalid
140.0ms	601×	body	512	valid
65.0ms	190×	body	1024	invalid
53.0ms	232×	body	512	invalid
49.0ms	308×	body	256	valid
29.0ms	175×	body	256	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 1892 to 1357 computations (28.3% saved)

Pareto

0.4338444299533953

Details

analyze949.0ms (8%)

sample61.0ms (0.5%)

simplify262.0ms (2.2%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite59.0ms (0.5%)

series686.0ms (5.8%)

simplify66.0ms (0.6%)

prune177.0ms (1.5%)

localize11.0ms (0.1%)

rewrite35.0ms (0.3%)

series654.0ms (5.5%)

simplify60.0ms (0.5%)

prune154.0ms (1.3%)

localize10.0ms (0.1%)

rewrite21.0ms (0.2%)

series638.0ms (5.4%)

simplify60.0ms (0.5%)

prune183.0ms (1.5%)

localize15.0ms (0.1%)

rewrite32.0ms (0.3%)

series1.3s (11.2%)

simplify83.0ms (0.7%)

prune310.0ms (2.6%)

simplify57.0ms (0.5%)

regimes748.0ms (6.3%)

bsearch0.0ms (0%)

regimes416.0ms (3.5%)

bsearch0.0ms (0%)

regimes83.0ms (0.7%)

bsearch0.0ms (0%)

regimes141.0ms (1.2%)

bsearch185.0ms (1.6%)

regimes93.0ms (0.8%)

bsearch126.0ms (1.1%)

regimes68.0ms (0.6%)

bsearch130.0ms (1.1%)

regimes66.0ms (0.6%)

bsearch139.0ms (1.2%)

regimes63.0ms (0.5%)

bsearch136.0ms (1.1%)

regimes63.0ms (0.5%)

bsearch37.0ms (0.3%)

regimes56.0ms (0.5%)

bsearch25.0ms (0.2%)

regimes25.0ms (0.2%)

bsearch15.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.3s (27.6%)

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