Details

analyze5.0s (9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5334	427
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Compiler

Compiled 41 to 33 computations (19.5% saved)

sample311.0ms (0.6%)

Algorithm

1×

intervals

Results

49.0ms	180×	body	128	valid
45.0ms	25×	body	2048	valid
40.0ms	37×	body	1024	nan
28.0ms	25×	body	1024	valid
27.0ms	100×	body	128	nan
23.0ms	16×	body	2048	nan
17.0ms	21×	body	512	nan
16.0ms	19×	body	512	valid
9.0ms	17×	body	256	nan
4.0ms	7×	body	256	valid

Compiler

Compiled 81 to 69 computations (14.8% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5613	61

prune14.0ms (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

52.1b

Counts

2 → 1

Compiler

Compiled 80 to 59 computations (26.3% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
15.1b	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
20.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
32.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite257.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`sqrt-div_binary64_3505`
60×	`associate-*r/_binary64_3430`
48×	`associate-*l/_binary64_3431`
46×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
43×	`*-un-lft-identity_binary64_3488`
36×	`frac-add_binary64_3496` `times-frac_binary64_3494` `frac-times_binary64_3498`
32×	`add-sqr-sqrt_binary64_3510`
31×	`add-cube-cbrt_binary64_3523`
24×	`pow1_binary64_3549`
22×	`flip3--_binary64_3492` `flip--_binary64_3463`
20×	`associate-/l/_binary64_3435` `distribute-neg-frac_binary64_3452`
16×	`distribute-lft-neg-in_binary64_3445` `distribute-rgt-neg-in_binary64_3446`
15×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `sqrt-prod_binary64_3504`
12×	`associate-/l*_binary64_3433` `pow-prod-down_binary64_3559`
6×	`distribute-lft-out_binary64_3439` `cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
5×	`associate-r_binary64_3428` `sqrt-pow1_binary64_3506`
4×	`unpow-prod-down_binary64_3567` `add-log-exp_binary64_3527` `neg-mul-1_binary64_3484`
3×	`associate-/r*_binary64_3432`
2×	`associate-/r/_binary64_3434` `pow1/2_binary64_3568`
1×	`distribute-lft-in_binary64_3437` `clear-num_binary64_3487` `distribute-rgt-in_binary64_3438` `distribute-lft-out--_binary64_3440` `associate-l_binary64_3429` `frac-2neg_binary64_3499` `*-commutative_binary64_3419` `div-exp_binary64_3539` `distribute-frac-neg_binary64_3451` `cbrt-undiv_binary64_3522` `neg-sub0_binary64_3483` `div-sub_binary64_3493` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

4 → 183

Calls

4 calls:

65.0ms	(.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
54.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
32.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

series16.9s (30.8%)

Counts

4 → 96

Calls

4 calls:

7.5s	(sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))
6.9s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
2.0s	(.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
602.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

Compiler

Compiled 19244 to 14632 computations (24% saved)

simplify501.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5116	32104

prune2.7s (4.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	257	22	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	22	280

Error

25.8b

Counts

280 → 22

Compiler

Compiled 27309 to 13173 computations (51.8% saved)

localize16.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 F A))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
13.8b	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3510`
17×	`associate-r_binary64_3428`
15×	`pow1_binary64_3549`
14×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
10×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `times-frac_binary64_3494`
9×	`associate-l_binary64_3429`
7×	`pow-prod-down_binary64_3559`
6×	`sqrt-pow1_binary64_3506` `sqrt-prod_binary64_3504`
4×	`unswap-sqr_binary64_3456` `associate-*r/_binary64_3430`
3×	`cbrt-unprod_binary64_3521` `add-log-exp_binary64_3527` `pow1/2_binary64_3568` `prod-exp_binary64_3537`
2×	`sqrt-div_binary64_3505` `*-commutative_binary64_3419`
1×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `sqrt-unprod_binary64_3508`

Counts

3 → 72

Calls

3 calls:

17.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
13.0ms	(*.f64 -1/2 (/.f64 F A))
7.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

series311.0ms (0.6%)

Counts

3 → 18

Calls

3 calls:

120.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A))))
108.0ms	(*.f64 -1/2 (/.f64 F A))
82.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 502 to 550 computations (-9.6% saved)

simplify159.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4948	1045
1	4948	1045

prune265.0ms (0.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	83	29	112

Error

25.7b

Counts

112 → 29

Compiler

Compiled 2282 to 1641 computations (28.1% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 F A))
0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2)))
13.8b	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

rewrite85.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_3510`
23×	`add-exp-log_binary64_3526` `associate-r_binary64_3428` `pow1_binary64_3549`
16×	`add-cbrt-cube_binary64_3524` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
11×	`cbrt-unprod_binary64_3521` `pow-prod-down_binary64_3559` `prod-exp_binary64_3537`
10×	`times-frac_binary64_3494`
8×	`cbrt-prod_binary64_3519` `associate-l_binary64_3429`
6×	`sqrt-prod_binary64_3504`
5×	`unswap-sqr_binary64_3456` `associate-*r/_binary64_3430`
4×	`add-log-exp_binary64_3527`
3×	`sqrt-div_binary64_3505` `*-commutative_binary64_3419`
2×	`associate-*l/_binary64_3431` `sqrt-pow1_binary64_3506`
1×	`pow1/2_binary64_3568` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`

Counts

4 → 95

Calls

4 calls:

29.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2))))
19.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2)))
13.0ms	(*.f64 -1/2 (/.f64 F A))
7.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

series502.0ms (0.9%)

Counts

4 → 24

Calls

4 calls:

168.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2)))
126.0ms	(*.f64 -1/2 (/.f64 F A))
116.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (cbrt.f64 (sqrt.f64 2))))
91.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 1050 to 1110 computations (-5.7% saved)

simplify128.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5397	1618

prune392.0ms (0.7%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	4	24	28
Picked	0	1	1
Done	0	0	0
Total	117	31	148

Error

25.7b

Counts

148 → 31

Compiler

Compiled 3621 to 2878 computations (20.5% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 F A))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))
13.8b	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

rewrite83.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_3510`
28×	`pow1_binary64_3549`
23×	`associate-r_binary64_3428` `sqrt-prod_binary64_3504`
19×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
17×	`pow-prod-down_binary64_3559`
16×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `associate-l_binary64_3429`
12×	`sqrt-pow1_binary64_3506`
10×	`times-frac_binary64_3494`
6×	`cbrt-unprod_binary64_3521` `pow1/2_binary64_3568` `prod-exp_binary64_3537`
5×	`unswap-sqr_binary64_3456` `associate-*r/_binary64_3430`
4×	`add-log-exp_binary64_3527`
3×	`sqrt-div_binary64_3505` `*-commutative_binary64_3419` `sqrt-unprod_binary64_3508`
2×	`associate-*l/_binary64_3431`
1×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`

Counts

4 → 105

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2))))
19.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))
13.0ms	(*.f64 -1/2 (/.f64 F A))
7.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

series449.0ms (0.8%)

Counts

4 → 24

Calls

4 calls:

138.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2)))
116.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F A))) (sqrt.f64 (sqrt.f64 2))))
106.0ms	(*.f64 -1/2 (/.f64 F A))
88.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F A)))

Compiler

Compiled 886 to 946 computations (-6.8% saved)

simplify170.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4887	1763
1	4887	1763

prune292.0ms (0.5%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	26	29
Picked	0	1	1
Done	0	1	1
Total	128	32	160

Error

25.7b

Counts

160 → 32

Compiler

Compiled 2289 to 1785 computations (22% saved)

regimes8.7s (15.9%)

Accuracy

Total 8.2b remaining (23.2%)

Threshold costs 0b (0%)

Compiler

Compiled 31492 to 23120 computations (26.6% saved)

bsearch20.0ms (0%)

Compiler: Compiled 40 to 32 computations (20% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	264	434
1	264	434

Compiler

Compiled 562 to 390 computations (30.6% saved)

end0.0ms (0%)

sample17.4s (31.7%)

Algorithm

1×

intervals

Results

1.5s	5562×	body	128	valid
1.0s	912×	body	1024	valid
961.0ms	842×	body	1024	nan
948.0ms	631×	body	2048	valid
871.0ms	589×	body	2048	nan
823.0ms	2967×	body	128	nan
478.0ms	557×	body	512	nan
455.0ms	555×	body	512	valid
199.0ms	339×	body	256	valid
189.0ms	342×	body	256	nan
2.0ms	1×	body	4096	valid

Compiler

Compiled 5350 to 3871 computations (27.6% saved)

Details

analyze5.0s (9%)

sample311.0ms (0.6%)

simplify69.0ms (0.1%)

prune14.0ms (0%)

localize42.0ms (0.1%)

rewrite257.0ms (0.5%)

series16.9s (30.8%)

simplify501.0ms (0.9%)

prune2.7s (4.9%)

localize16.0ms (0%)

rewrite46.0ms (0.1%)

series311.0ms (0.6%)

simplify159.0ms (0.3%)

prune265.0ms (0.5%)

localize24.0ms (0%)

rewrite85.0ms (0.2%)

series502.0ms (0.9%)

simplify128.0ms (0.2%)

prune392.0ms (0.7%)

localize21.0ms (0%)

rewrite83.0ms (0.2%)

series449.0ms (0.8%)

simplify170.0ms (0.3%)

prune292.0ms (0.5%)

regimes8.7s (15.9%)

bsearch20.0ms (0%)

simplify61.0ms (0.1%)

end0.0ms (0%)

sample17.4s (31.7%)

Profiling