Details

sample285.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
7.0ms	35×	body	2560	valid
5.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 33.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

23.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune306.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	7	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 5.8b

Counts

113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

15.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	479	897
1	2066	778
2	5003	729

prune298.0ms

Filtered

116 candidates to 90 candidates (77.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	117	7	124

Merged error: 5.8b

Counts

124 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`add-exp-log` `associate-l`
11×	`times-frac`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`distribute-rgt-neg-in` `associate-r`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `div-exp` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `distribute-rgt-in` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 105

Calls

4 calls:

14.0ms	(* (/ 1 a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (/ 1 a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	517	885
1	2397	770
2	5003	745

prune298.0ms

Filtered

117 candidates to 91 candidates (77.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	116	8	124

Merged error: 5.7b

Counts

124 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
11.6b	(+ (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`fma-def` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `flip3-+` `fma-neg` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 75

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(+ (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(+ (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	268	620
1	998	515
2	3876	499
3	5001	497

prune297.0ms

Filtered

87 candidates to 75 candidates (86.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	87	8	95

Merged error: 5.7b

Counts

95 → 8

regimes250.0ms

Accuracy

85.5% (4.2b remaining)

Error of 9.6b against oracle of 5.5b and baseline of 34.2b

bsearch52.0ms

Steps

Iters	Range		Point
1	1.5436983288905166e-76	1.715917488860867e-76	1.5867531188831042e-76
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample975.0ms

Algorithm

intervals

Results

216.0ms	1105×	body	2560	valid
181.0ms	5783×	body	80	valid
139.0ms	898×	body	1280	valid
88.0ms	2921×	body	80	nan
56.0ms	460×	body	640	valid
24.0ms	105×	body	5120	valid
22.0ms	226×	body	320	valid
7.0ms	124×	body	160	valid