Details

analyze894.0ms (7.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4877	216
1	4877	216
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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample45.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	22×	body	128	nan
2.0ms	20×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify351.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (345.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune8.0ms (0.1%)

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

19.4b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite152.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

19.4b

Rules

13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

11.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 2821 to 1660 computations (41.2% saved)

series763.0ms (6.3%)

Error

5.4b

Counts

4 → 72

Calls

4 calls:

177.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
175.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
157.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 7100 to 4884 computations (31.2% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4967	2448
1	4967	2448

prune244.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	8	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Error

5.3b

Counts

132 → 8

Compiler

Compiled 5515 to 3148 computations (42.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite144.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`sqrt-prod_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 2917 to 1611 computations (44.8% saved)

series901.0ms (7.4%)

Error

5.3b

Counts

4 → 71

Calls

4 calls:

305.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
190.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
165.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
161.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

Compiler

Compiled 5416 to 3765 computations (30.5% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4941	2842
1	4941	2842

prune197.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	5	143
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Error

5.3b

Counts

151 → 8

Compiler

Compiled 4849 to 2532 computations (47.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite155.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`sqrt-prod_binary64` `unswap-sqr_binary64` `associate-l_binary64`
2×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `flip3-+_binary64` `flip-+_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3424 to 1864 computations (45.6% saved)

series771.0ms (6.3%)

Error

5.3b

Counts

4 → 71

Calls

4 calls:

211.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
172.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
166.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5688 to 4046 computations (28.9% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4938	2781
1	4938	2781

prune210.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	151	8	159

Error

5.3b

Counts

159 → 8

Compiler

Compiled 5321 to 2898 computations (45.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
1.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite279.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

96×	`times-frac_binary64`
80×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`sqrt-prod_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r/_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 127

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5668 to 3121 computations (44.9% saved)

series794.0ms (6.5%)

Error

5.3b

Counts

4 → 71

Calls

4 calls:

214.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
173.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
170.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
153.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5688 to 4039 computations (29% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4995	5024
1	4995	5024

prune1.8s (14.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	197	9	206

Error

5.3b

Counts

206 → 9

Compiler

Compiled 7145 to 3787 computations (47% saved)

regimes972.0ms (8%)

Accuracy

Total 1.6b remaining (21%)

Threshold costs 0b (0%)

Compiler

Compiled 10670 to 7570 computations (29.1% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	169	463
1	169	463

end0.0ms (0%)

sample3.1s (25.4%)

Algorithm

1×

intervals

Results

680.0ms	8000×	body	128	valid
58.0ms	675×	body	128	nan
31.0ms	383×	body	128	invalid

Compiler

Compiled 2992 to 2093 computations (30% saved)

Details

analyze894.0ms (7.4%)

sample45.0ms (0.4%)

simplify351.0ms (2.9%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite152.0ms (1.3%)

series763.0ms (6.3%)

simplify67.0ms (0.6%)

prune244.0ms (2%)

localize22.0ms (0.2%)

rewrite144.0ms (1.2%)

series901.0ms (7.4%)

simplify68.0ms (0.6%)

prune197.0ms (1.6%)

localize26.0ms (0.2%)

rewrite155.0ms (1.3%)

series771.0ms (6.3%)

simplify66.0ms (0.5%)

prune210.0ms (1.7%)

localize23.0ms (0.2%)

rewrite279.0ms (2.3%)

series794.0ms (6.5%)

simplify87.0ms (0.7%)

prune1.8s (14.7%)

regimes972.0ms (8%)

bsearch7.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.1s (25.4%)

Profiling