Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	195×	body	80	valid
6.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
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	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

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

localize13.0ms

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)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune234.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	12	83

Merged error: 5.9b

Counts

83 → 12

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)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
3×	`distribute-rgt-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-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(+ (- 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)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	368	755
1	1544	656
2	5002	644

prune227.0ms

Filtered

81 candidates to 61 candidates (75.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	78	15	93

Merged error: 5.8b

Counts

93 → 15

localize17.0ms

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)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`div-exp`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv`
3×	`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-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `associate-/r/` `flip-+` `div-inv` `inv-pow`

Counts

4 → 75

Calls

4 calls:

14.0ms	(/ 1 (* 3.0 (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
8.0ms	(+ (- 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)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (* 3.0 (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	411	815
1	1729	698
2	5001	680

prune218.0ms

Filtered

87 candidates to 57 candidates (65.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	87	15	102

Merged error: 5.8b

Counts

102 → 15

localize17.0ms

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)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

681×	`times-frac`
457×	`*-un-lft-identity`
286×	`add-sqr-sqrt`
285×	`add-cube-cbrt`
86×	`distribute-lft-out`
43×	`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×	`add-log-exp`
8×	`cbrt-undiv`
5×	`pow1`
3×	`sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 373

Calls

4 calls:

21.0ms	(/ (/ 1 3.0) (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
8.0ms	(+ (- 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)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (/ 1 3.0) (/ a (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
50.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

385 → 385

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1561	7436
1	5001	6965

prune734.0ms

Filtered

385 candidates to 186 candidates (48.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	381	4	385
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	387	13	400

Merged error: 5.8b

Counts

400 → 13

regimes520.0ms

Accuracy

88.5% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 34.3b

bsearch177.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	8.282729022252948e+102
7	2.4861480825170347e-112	4.9053706167200877e-110	2.548256466828356e-112
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

8.282729022252948e+102

2.4861480825170347e-112

4.9053706167200877e-110

2.548256466828356e-112

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	33
1	55	33
2	55	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	1104×	body	2560	valid
205.0ms	5787×	body	80	valid
153.0ms	898×	body	1280	valid
98.0ms	2923×	body	80	nan
71.0ms	458×	body	640	valid
27.0ms	105×	body	5120	valid
24.0ms	226×	body	320	valid
8.0ms	123×	body	160	valid