Details

analyze605.0ms (13.4%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
5.0ms	110×	body	128	invalid

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify172.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4898	19
1	4898	19

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.6b

Counts

2 → 2

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
1.4b	(-.f64 (.f64 z z) (.f64 x x))
13.8b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_18173`
15×	`*-un-lft-identity_binary64_18151`
13×	`times-frac_binary64_18157` `add-cube-cbrt_binary64_18186`
7×	`difference-of-squares_binary64_18120` `add-log-exp_binary64_18190`
5×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
4×	`associate-/l*_binary64_18096` `cancel-sign-sub-inv_binary64_18117`
3×	`flip3--_binary64_18155` `pow1_binary64_18212` `flip--_binary64_18126` `associate-/r*_binary64_18095`
2×	`diff-log_binary64_18243` `associate-/l/_binary64_18098` `sub-neg_binary64_18144` `div-sub_binary64_18156`
1×	`div-exp_binary64_18202` `div-inv_binary64_18148` `distribute-lft-out--_binary64_18103` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `associate--l-_binary64_18089` `cbrt-undiv_binary64_18185`

Counts

3 → 65

Calls

3 calls:

11.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
7.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
4.0ms	(-.f64 (.f64 z z) (.f64 x x))

series103.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
35.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
22.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5012	1382

prune71.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Error

0.0b

Counts

76 → 4

Compiler

Compiled 1515 to 434 computations (71.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (-.f64 z x))
0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

rewrite78.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`times-frac_binary64_18157`
165×	`*-un-lft-identity_binary64_18151`
128×	`add-sqr-sqrt_binary64_18173`
81×	`add-cube-cbrt_binary64_18186`
26×	`associate-/r*_binary64_18095`
22×	`distribute-lft-out_binary64_18102` `difference-of-squares_binary64_18120`
20×	`distribute-lft-out--_binary64_18103`
13×	`associate-/r/_binary64_18097`
10×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
7×	`div-inv_binary64_18148` `flip3--_binary64_18155` `associate-/l*_binary64_18096` `flip--_binary64_18126`
5×	`add-log-exp_binary64_18190`
4×	`div-exp_binary64_18202` `cbrt-undiv_binary64_18185`
3×	`pow1_binary64_18212` `cancel-sign-sub-inv_binary64_18117`
2×	`associate-/l/_binary64_18098` `clear-num_binary64_18150` `frac-2neg_binary64_18162`
1×	`diff-log_binary64_18243` `flip-+_binary64_18125` `sub-neg_binary64_18144` `flip3-+_binary64_18154`

Counts

3 → 181

Calls

3 calls:

36.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
13.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
6.0ms	(/.f64 y (-.f64 z x))

series113.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
38.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
31.0ms	(/.f64 y (-.f64 z x))

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4976	4391
1	4976	4391

prune152.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

Counts

194 → 6

Compiler

Compiled 4324 to 1064 computations (75.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
0.0b	(/.f64 (-.f64 z x) y)
0.2b	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_18173`
40×	`*-un-lft-identity_binary64_18151`
31×	`times-frac_binary64_18157`
24×	`add-cube-cbrt_binary64_18186`
19×	`associate-r_binary64_18091`
10×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
7×	`distribute-lft-out--_binary64_18103` `difference-of-squares_binary64_18120`
5×	`pow1_binary64_18212` `associate-/l*_binary64_18096` `add-log-exp_binary64_18190`
4×	`associate-l_binary64_18092`
3×	`cancel-sign-sub-inv_binary64_18117` `associate-/r*_binary64_18095`
2×	`div-exp_binary64_18202` `div-inv_binary64_18148` `flip3--_binary64_18155` `associate-*l/_binary64_18094` `associate-/l/_binary64_18098` `unswap-sqr_binary64_18119` `flip-+_binary64_18125` `flip--_binary64_18126` `frac-times_binary64_18161` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184` `cbrt-undiv_binary64_18185` `flip3-+_binary64_18154`
1×	`diff-log_binary64_18243` `distribute-lft-out_binary64_18102` `associate-r/_binary64_18093` `pow-prod-down_binary64_18222` `-commutative_binary64_18082` `sub-neg_binary64_18144` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `div-sub_binary64_18156`

Counts

3 → 95

Calls

3 calls:

13.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
11.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
7.0ms	(/.f64 (-.f64 z x) y)

series108.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
41.0ms	(-.f64 (*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y)) y)
24.0ms	(/.f64 (-.f64 z x) y)

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4956	1642
1	4956	1642

prune78.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	104	6	110

Error

Counts

110 → 6

Compiler

Compiled 2104 to 610 computations (71% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 z x) y)
0.0b	(/.f64 1 (-.f64 z x))
0.0b	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
0.3b	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))

rewrite225.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

895×	`times-frac_binary64_18157`
607×	`*-un-lft-identity_binary64_18151`
488×	`add-sqr-sqrt_binary64_18173`
353×	`add-cube-cbrt_binary64_18186`
70×	`distribute-lft-out_binary64_18102`
62×	`difference-of-squares_binary64_18120`
56×	`distribute-lft-out--_binary64_18103`
42×	`div-inv_binary64_18148`
37×	`associate-/r/_binary64_18097`
32×	`add-exp-log_binary64_18189`
29×	`associate-/r*_binary64_18095`
23×	`associate-/l*_binary64_18096`
20×	`add-cbrt-cube_binary64_18187`
19×	`div-exp_binary64_18202` `flip3--_binary64_18155` `flip--_binary64_18126`
10×	`cbrt-undiv_binary64_18185`
6×	`add-log-exp_binary64_18190`
5×	`pow1_binary64_18212`
3×	`1-exp_binary64_18195` `rec-exp_binary64_18201` `associate-/l/_binary64_18098` `cancel-sign-sub-inv_binary64_18117` `clear-num_binary64_18150` `frac-2neg_binary64_18162`
1×	`inv-pow_binary64_18236` `diff-log_binary64_18243` `pow-flip_binary64_18225` `flip-+_binary64_18125` `sub-neg_binary64_18144` `flip3-+_binary64_18154`

Counts

4 → 493

Calls

4 calls:

119.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
21.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
6.0ms	(/.f64 1 (-.f64 z x))
5.0ms	(/.f64 (+.f64 z x) y)

series127.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
36.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
24.0ms	(/.f64 (+.f64 z x) y)
22.0ms	(/.f64 1 (-.f64 z x))

simplify216.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

505 → 505

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4966	15070
1	4966	15070

prune690.0ms (15.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	505	0	505
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	505	6	511

Error

Counts

511 → 6

Compiler

Compiled 13141 to 3847 computations (70.7% saved)

regimes297.0ms (6.6%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Compiler

Compiled 4126 to 2356 computations (42.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms (0%)

sample1.1s (24.9%)

Algorithm

1×

intervals

Results

335.0ms	8000×	body	128	valid
119.0ms	2885×	body	128	invalid

Compiler

Compiled 615 to 361 computations (41.3% saved)

Details

analyze605.0ms (13.4%)

sample27.0ms (0.6%)

simplify172.0ms (3.8%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite27.0ms (0.6%)

series103.0ms (2.3%)

simplify56.0ms (1.2%)

prune71.0ms (1.6%)

localize8.0ms (0.2%)

rewrite78.0ms (1.7%)

series113.0ms (2.5%)

simplify93.0ms (2.1%)

prune152.0ms (3.4%)

localize9.0ms (0.2%)

rewrite42.0ms (0.9%)

series108.0ms (2.4%)

simplify71.0ms (1.6%)

prune78.0ms (1.7%)

localize9.0ms (0.2%)

rewrite225.0ms (5%)

series127.0ms (2.8%)

simplify216.0ms (4.8%)

prune690.0ms (15.3%)

regimes297.0ms (6.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (24.9%)

Profiling