Details

analyze938.0ms (11.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	80
1	1992	80
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	51×	body	2048	valid
7.0ms	160×	body	128	valid
4.0ms	22×	body	1024	valid
2.0ms	13×	body	512	valid
2.0ms	9×	body	4096	valid
1.0ms	19×	body	128	nan
1.0ms	12×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune5.0ms (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

35.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite151.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate--l-_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2360 to 368 computations (84.4% saved)

series705.0ms (8.4%)

Error

4.9b

Counts

4 → 74

Calls

4 calls:

206.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
170.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
147.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
125.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3002 to 2103 computations (29.9% saved)

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4939	3526
1	4939	3526

prune136.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	159	11	170
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	11	171

Error

4.9b

Counts

171 → 11

Compiler

Compiled 3244 to 699 computations (78.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.2b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
10.4b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite158.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`sqrt-prod_binary64` `associate-/r/_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`sqrt-div_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64` `diff-log_binary64` `sub-neg_binary64`

Counts

4 → 129

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3886 to 521 computations (86.6% saved)

series885.0ms (10.5%)

Error

4.9b

Counts

4 → 72

Calls

4 calls:

288.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
261.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
145.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
136.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3750 to 2344 computations (37.5% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5069	5129

prune152.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	206	6	212

Error

4.9b

Counts

212 → 6

Compiler

Compiled 4580 to 845 computations (81.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.5b	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite163.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

55×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`
23×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64`
3×	`distribute-rgt-neg-in_binary64` `associate-/r*_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `div-inv_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-sub_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 113

Calls

4 calls:

40.0ms	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
6.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3146 to 471 computations (85% saved)

series712.0ms (8.4%)

Error

4.9b

Counts

4 → 73

Calls

4 calls:

217.0ms	(-.f64 (/.f64 b_2 (neg.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))
178.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)
138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
129.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3199 to 2101 computations (34.3% saved)

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4953	3812
1	4953	3812

prune130.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	186	6	192

Error

4.9b

Counts

192 → 6

Compiler

Compiled 3742 to 671 computations (82.1% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 c b_2))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-l_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `div-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

1 → 32

Calls

1 calls:

7.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 373 to 195 computations (47.7% saved)

series59.0ms (0.7%)

Error

4.9b

Counts

1 → 6

Calls

1 calls:

56.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 90 to 88 computations (2.2% saved)

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5015	369

prune26.0ms (0.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	30	8	38
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	31	13	44

Error

4.9b

Counts

44 → 13

Compiler

Compiled 356 to 175 computations (50.8% saved)

regimes1.4s (16.1%)

Accuracy

Total 3.3b remaining (37.3%)

Threshold costs 0b (0%)

Compiler

Compiled 6180 to 3731 computations (39.6% saved)

bsearch71.0ms (0.8%)

Steps

Iters	Range		Point
7	1.669109912800578e+16	2.419244773117199e+18	2.354428103312287e+18
3	-1.0066960536968472e-260	-7.330184670040939e-261	-7.4406991673960255e-261
9	-1.305429404777108e-12	-3.585820180615719e-20	-9.262564350171407e-13

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	88
1	104	88

end0.0ms (0%)

sample2.2s (26.6%)

Algorithm

1×

intervals

Results

241.0ms	1144×	body	2048	valid
231.0ms	5191×	body	128	valid
116.0ms	702×	body	1024	valid
110.0ms	403×	body	4096	valid
45.0ms	379×	body	512	valid
34.0ms	780×	body	128	nan
15.0ms	181×	body	256	valid
11.0ms	261×	body	128	invalid

Compiler

Compiled 1560 to 945 computations (39.4% saved)

Details

analyze938.0ms (11.1%)

sample42.0ms (0.5%)

simplify74.0ms (0.9%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite151.0ms (1.8%)

series705.0ms (8.4%)

simplify85.0ms (1%)

prune136.0ms (1.6%)

localize10.0ms (0.1%)

rewrite158.0ms (1.9%)

series885.0ms (10.5%)

simplify78.0ms (0.9%)

prune152.0ms (1.8%)

localize13.0ms (0.2%)

rewrite163.0ms (1.9%)

series712.0ms (8.4%)

simplify85.0ms (1%)

prune130.0ms (1.5%)

localize4.0ms (0%)

rewrite31.0ms (0.4%)

series59.0ms (0.7%)

simplify100.0ms (1.2%)

prune26.0ms (0.3%)

regimes1.4s (16.1%)

bsearch71.0ms (0.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (26.6%)

Profiling