Details

analyze2.6s (7.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4881	464
1	4881	464
0	6	6
1	6	6

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

Symmetry

(sort z t)

Compiler

Compiled 20 to 20 computations (0% saved)

sample155.0ms (0.5%)

Algorithm

1×

intervals

Results

39.0ms	55×	body	1024	valid
21.0ms	25×	body	2048	valid
21.0ms	151×	body	128	valid
11.0ms	78×	body	128	nan
7.0ms	16×	body	512	valid
4.0ms	30×	body	128	invalid
3.0ms	9×	body	256	valid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune5.0ms (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

19.8b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.3b	(/.f64 a (*.f64 b 3))
0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
24.2b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite326.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

17.7b

Rules

19×	`add-exp-log_binary64_18189` `add-cbrt-cube_binary64_18187`
11×	`add-cube-cbrt_binary64_18186` `add-sqr-sqrt_binary64_18173` `*-un-lft-identity_binary64_18151`
9×	`times-frac_binary64_18157` `pow1_binary64_18212`
8×	`cos-sum_binary64_18285`
7×	`cancel-sign-sub-inv_binary64_18117`
5×	`prod-exp_binary64_18200` `cbrt-unprod_binary64_18184`
4×	`add-log-exp_binary64_18190` `div-exp_binary64_18202` `cbrt-undiv_binary64_18185` `associate-/l_binary64_18096` `associate-/r_binary64_18095`
3×	`cos-diff_binary64_18288` `div-inv_binary64_18148` `pow-prod-down_binary64_18222` `associate-r_binary64_18091`
2×	`frac-2neg_binary64_18162` `clear-num_binary64_18150`
1×	`sub-neg_binary64_18144` `distribute-rgt-in_binary64_18101` `distribute-lft-in_binary64_18100` `associate-l_binary64_18092` `*-commutative_binary64_18082`

Counts

4 → 78

Calls

4 calls:

16.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
13.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
8.0ms	(/.f64 (*.f64 z t) 3)
7.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 2173 to 1334 computations (38.6% saved)

series981.0ms (3%)

Error

15.5b

Counts

4 → 45

Calls

4 calls:

492.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
187.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
108.0ms	(/.f64 a (*.f64 b 3))
98.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 2890 to 2315 computations (19.9% saved)

simplify136.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4932	1991
1	4932	1991

prune367.0ms (1.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	101	22	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	22	124

Error

14.6b

Counts

124 → 22

Compiler

Compiled 3427 to 2207 computations (35.6% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.3b	(/.f64 a (*.f64 b 3))

rewrite169.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

13×	`add-exp-log_binary64_18189` `add-cbrt-cube_binary64_18187`
8×	`pow1_binary64_18212` `add-cube-cbrt_binary64_18186` `add-sqr-sqrt_binary64_18173` `*-un-lft-identity_binary64_18151`
7×	`cancel-sign-sub-inv_binary64_18117`
6×	`times-frac_binary64_18157`
5×	`add-log-exp_binary64_18190`
4×	`prod-exp_binary64_18200` `cbrt-unprod_binary64_18184`
3×	`associate-/l_binary64_18096` `pow-prod-down_binary64_18222` `associate-r*_binary64_18091`
2×	`div-exp_binary64_18202` `cbrt-undiv_binary64_18185` `div-inv_binary64_18148`
1×	`frac-2neg_binary64_18162` `clear-num_binary64_18150` `associate-/r_binary64_18095` `associate-l_binary64_18092` `-commutative_binary64_18082` `diff-log_binary64_18243` `flip3--_binary64_18155` `sub-neg_binary64_18144` `flip--_binary64_18126`

Counts

3 → 57

Calls

3 calls:

16.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
12.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
7.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1174 to 678 computations (42.2% saved)

series832.0ms (2.5%)

Error

14.3b

Counts

3 → 32

Calls

3 calls:

542.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
134.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
110.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1123 to 1034 computations (7.9% saved)

simplify153.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4915	1209
1	4915	1209

prune237.0ms (0.7%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	6	15	21
Picked	1	0	1
Done	0	0	0
Total	83	28	111

Error

14.3b

Counts

111 → 28

Compiler

Compiled 2022 to 1292 computations (36.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 b (/.f64 a 3))
0.5b	(/.f64 1 (/.f64 b (/.f64 a 3)))

rewrite1.6s (4.9%)

Algorithm

1×	rewrite-expression-head

Error

14.3b

Rules

801×	`times-frac_binary64_18157`
382×	`add-cube-cbrt_binary64_18186` `add-sqr-sqrt_binary64_18173` `*-un-lft-identity_binary64_18151`
137×	`cancel-sign-sub-inv_binary64_18117`
57×	`associate-/r*_binary64_18095`
35×	`add-exp-log_binary64_18189` `div-inv_binary64_18148`
23×	`add-cbrt-cube_binary64_18187`
18×	`div-exp_binary64_18202`
10×	`pow1_binary64_18212` `associate-/r/_binary64_18097`
9×	`cbrt-undiv_binary64_18185`
6×	`add-log-exp_binary64_18190` `associate-/l*_binary64_18096`
3×	`1-exp_binary64_18195` `rec-exp_binary64_18201` `pow-prod-down_binary64_18222` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184` `associate-r_binary64_18091`
2×	`frac-2neg_binary64_18162` `clear-num_binary64_18150`
1×	`inv-pow_binary64_18236` `pow-flip_binary64_18225` `associate-l_binary64_18092` `*-commutative_binary64_18082` `diff-log_binary64_18243` `flip3--_binary64_18155` `sub-neg_binary64_18144` `flip--_binary64_18126`

Counts

4 → 440

Calls

4 calls:

72.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
29.0ms	(/.f64 1 (/.f64 b (/.f64 a 3)))
12.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
11.0ms	(/.f64 b (/.f64 a 3))

Compiler

Compiled 12475 to 7918 computations (36.5% saved)

series989.0ms (3%)

Error

14.3b

Counts

4 → 38

Calls

4 calls:

590.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 1 (/.f64 b (/.f64 a 3))))
136.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
110.0ms	(/.f64 1 (/.f64 b (/.f64 a 3)))
106.0ms	(/.f64 b (/.f64 a 3))

Compiler

Compiled 1433 to 1327 computations (7.4% saved)

simplify241.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5509	10650

prune1.4s (4.2%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	478	0	478
Fresh	0	27	27
Picked	0	1	1
Done	0	0	0
Total	478	28	506

Error

14.3b

Counts

506 → 28

Compiler

Compiled 11864 to 6909 computations (41.8% saved)

localize28.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 (/.f64 a b) 3)

rewrite375.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

14.3b

Rules

141×	`times-frac_binary64_18157`
81×	`add-cube-cbrt_binary64_18186` `add-sqr-sqrt_binary64_18173` `*-un-lft-identity_binary64_18151`
43×	`cancel-sign-sub-inv_binary64_18117`
13×	`add-exp-log_binary64_18189` `add-cbrt-cube_binary64_18187` `associate-/l*_binary64_18096`
9×	`div-inv_binary64_18148`
8×	`pow1_binary64_18212`
5×	`add-log-exp_binary64_18190`
3×	`div-exp_binary64_18202` `cbrt-undiv_binary64_18185` `associate-/r_binary64_18095` `pow-prod-down_binary64_18222` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184` `associate-r*_binary64_18091`
1×	`frac-2neg_binary64_18162` `clear-num_binary64_18150` `associate-/l/_binary64_18098` `associate-l_binary64_18092` `*-commutative_binary64_18082` `diff-log_binary64_18243` `flip3--_binary64_18155` `sub-neg_binary64_18144` `flip--_binary64_18126`

Counts

3 → 142

Calls

3 calls:

35.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
12.0ms	(/.f64 (/.f64 a b) 3)
12.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

Compiler

Compiled 3320 to 1701 computations (48.8% saved)

series817.0ms (2.5%)

Error

14.3b

Counts

3 → 32

Calls

3 calls:

539.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
124.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
113.0ms	(/.f64 (/.f64 a b) 3)

Compiler

Compiled 1123 to 1027 computations (8.5% saved)

simplify143.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5215	2940

prune296.0ms (0.9%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	26	26
Picked	0	1	1
Done	0	1	1
Total	174	28	202

Error

14.3b

Counts

202 → 28

Compiler

Compiled 3238 to 1584 computations (51.1% saved)

regimes10.6s (32.1%)

Accuracy

Total 1.8b remaining (11.1%)

Threshold costs 0b (0%)

Compiler

Compiled 58341 to 53372 computations (8.5% saved)

bsearch11.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	122	111
1	122	111

Remove

(sort z t)

Compiler

Compiled 144 to 100 computations (30.6% saved)

end0.0ms (0%)

sample10.3s (31.4%)

Algorithm

1×

intervals

Results

1.0s	1607×	body	1024	valid
676.0ms	4612×	body	128	valid
625.0ms	703×	body	2048	valid
362.0ms	733×	body	512	valid
347.0ms	2339×	body	128	nan
159.0ms	1114×	body	128	invalid
118.0ms	345×	body	256	valid

Compiler

Compiled 3384 to 3066 computations (9.4% saved)

Details

analyze2.6s (7.8%)

sample155.0ms (0.5%)

simplify92.0ms (0.3%)

prune5.0ms (0%)

localize29.0ms (0.1%)

rewrite326.0ms (1%)

series981.0ms (3%)

simplify136.0ms (0.4%)

prune367.0ms (1.1%)

localize20.0ms (0.1%)

rewrite169.0ms (0.5%)

series832.0ms (2.5%)

simplify153.0ms (0.5%)

prune237.0ms (0.7%)

localize24.0ms (0.1%)

rewrite1.6s (4.9%)

series989.0ms (3%)

simplify241.0ms (0.7%)

prune1.4s (4.2%)

localize28.0ms (0.1%)

rewrite375.0ms (1.1%)

series817.0ms (2.5%)

simplify143.0ms (0.4%)

prune296.0ms (0.9%)

regimes10.6s (32.1%)

bsearch11.0ms (0%)

simplify27.0ms (0.1%)

end0.0ms (0%)

sample10.3s (31.4%)

Profiling