Details

sample378.0ms

Algorithm

intervals

Results

290.0ms	33×	body	1280	valid
24.0ms	44×	body	2560	valid
13.0ms	169×	body	80	valid
6.0ms	89×	body	80	nan
5.0ms	16×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify776.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 38.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b	(- (* b_2 b_2) (* a c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

19.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5743	1409

prune217.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 6.2b

Counts

97 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.8b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
26.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

10.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
16.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
83.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4948	2297
1	4948	2297

prune261.0ms

Filtered

98 candidates to 126 candidates (-28.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	125	10	135

Merged error: 5.9b

Counts

135 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
1.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
26.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 72

Calls

4 calls:

14.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5326	1113

prune207.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	83	11	94

Merged error: 5.8b

Counts

94 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.2b	(- (* b_2 b_2) (* a c))
1.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
26.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 50

Calls

4 calls:

2.0ms	(cbrt c)
8.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt c)
14.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5228	583

prune128.0ms

Filtered

47 candidates to 62 candidates (-31.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	6	7
Picked	1	0	1
Done	0	3	3
Total	62	11	73

Merged error: 5.8b

Counts

73 → 11

regimes665.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.7b against oracle of 5.4b and baseline of 29.9b

bsearch122.0ms

Steps

Iters	Range	Point
5	1.1994113433831075e+59	2.551497614016684e+59	1.9930311221408239e+59
7	-1.5288248722247393e-196	-2.8030120978369076e-198	-2.8405866436241524e-198
8	-9.755383452814402e+129	-1.823895620004969e+126	-1.95155870856424e+129

Iters

Range

Point

1.1994113433831075e+59

2.551497614016684e+59

1.9930311221408239e+59

-1.5288248722247393e-196

-2.8030120978369076e-198

-2.8405866436241524e-198

-9.755383452814402e+129

-1.823895620004969e+126

-1.95155870856424e+129

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	62
1	90	62

end0.0ms

sample2.6s

Algorithm

intervals

Results

525.0ms	1086×	body	2560	valid
462.0ms	5799×	body	80	valid
349.0ms	884×	body	1280	valid
224.0ms	2930×	body	80	nan
138.0ms	456×	body	640	valid
59.0ms	260×	body	320	valid
57.0ms	99×	body	5120	valid
18.0ms	118×	body	160	valid

Details

sample378.0ms

simplify776.0ms

prune19.0ms

localize32.0ms

rewrite59.0ms

series109.0ms

simplify90.0ms

prune217.0ms

localize19.0ms

rewrite61.0ms

series206.0ms

simplify86.0ms

prune261.0ms

localize18.0ms

rewrite48.0ms

series148.0ms

simplify88.0ms

prune207.0ms

localize27.0ms

rewrite33.0ms

series106.0ms

simplify47.0ms

prune128.0ms

regimes665.0ms

bsearch122.0ms

simplify3.0ms

end0.0ms

sample2.6s

Profiling