Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	195×	body	80	valid
6.0ms	33×	body	1280	valid
3.0ms	9×	body	640	valid
3.0ms	97×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune279.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	11	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	11	103

Merged error: 5.9b

Counts

103 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

11.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	399	830
1	1688	721
2	5001	704

prune280.0ms

Filtered

101 candidates to 80 candidates (79.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	99	13	112

Merged error: 5.8b

Counts

112 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 3.0 (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

18.0ms	(/ 1 (* 3.0 (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ 1 (* 3.0 (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
50.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	442	892
1	1862	765
2	5001	748

prune274.0ms

Filtered

107 candidates to 76 candidates (71.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	106	14	120

Merged error: 5.8b

Counts

120 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 3.0) (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

681×	`times-frac`
460×	`*-un-lft-identity`
289×	`add-sqr-sqrt`
288×	`add-cube-cbrt`
86×	`distribute-lft-out`
46×	`distribute-rgt-neg-in`
37×	`div-inv`
29×	`associate-/r/`
26×	`add-exp-log`
21×	`associate-/r*`
16×	`div-exp` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`associate-/l*`
10×	`fma-def` `add-log-exp`
8×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 393

Calls

4 calls:

21.0ms	(/ (/ 1 3.0) (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ 1 3.0) (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1592	7513
1	5001	7036

prune772.0ms

Filtered

405 candidates to 205 candidates (50.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	402	3	405
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	406	13	419

Merged error: 5.8b

Counts

419 → 13

regimes417.0ms

Accuracy

88% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 34.4b

bsearch177.0ms

Steps

Iters	Range	Point
8	3.9532145147442873e+71	1.0218572913399418e+74	7.74705576891063e+72
8	1.0645440808835145e-134	7.540505695525985e-132	2.5643996228054395e-134
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

3.9532145147442873e+71

1.0218572913399418e+74

7.74705576891063e+72

1.0645440808835145e-134

7.540505695525985e-132

2.5643996228054395e-134

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	35
1	56	35
2	56	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

233.0ms	1104×	body	2560	valid
213.0ms	5787×	body	80	valid
160.0ms	898×	body	1280	valid
98.0ms	2923×	body	80	nan
64.0ms	458×	body	640	valid
27.0ms	105×	body	5120	valid
23.0ms	226×	body	320	valid
12.0ms	123×	body	160	valid