Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	35×	body	2560	valid
11.0ms	195×	body	80	valid
9.0ms	33×	body	1280	valid
5.0ms	97×	body	80	nan
2.0ms	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	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)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `div-sub` `clear-num` `div-inv`

Counts

4 → 30

Calls

4 calls:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify131.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	315	330
1	1125	302
2	4713	290
3	5001	290

prune110.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	33	9	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	9	43

Merged error: 5.9b

Counts

43 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`associate-l`
2×	`flip3--` `fma-neg` `sqrt-div` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 25

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	223	249
1	828	227
2	3445	217
3	5003	215

prune88.0ms

Filtered

37 candidates to 22 candidates (59.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	37	9	46

Merged error: 5.8b

Counts

46 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
2×	`flip3--` `fma-neg` `sqrt-div` `associate-/r*` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `flip3-+` `pow1/2` `clear-num` `flip-+` `div-inv` `inv-pow`

Counts

4 → 28

Calls

4 calls:

3.0ms	(/ 1 (* 3.0 a))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (* 3.0 a))
103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
52.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify138.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (134.0ms)

Iter	Nodes	Cost
0	236	252
1	888	230
2	4153	220
3	5001	218

prune94.0ms

Filtered

40 candidates to 25 candidates (62.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	38	11	49

Merged error: 5.8b

Counts

49 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
3×	`associate-/l/`
2×	`flip3--` `frac-2neg` `fma-neg` `sqrt-div` `clear-num` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `flip3-+` `pow1/2` `flip-+` `associate-/l*`

Counts

4 → 29

Calls

4 calls:

3.0ms	(/ (/ 1 3.0) a)
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ 1 3.0) a)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify150.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	242	256
1	924	232
2	4482	222
3	5001	221

prune86.0ms

Filtered

41 candidates to 23 candidates (56.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	41	11	52

Merged error: 5.8b

Counts

52 → 11

regimes423.0ms

Accuracy

88.1% (3.4b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 34.3b

bsearch162.0ms

Steps

Iters	Range	Point
8	3.9532145147442873e+71	1.0218572913399418e+74	3.3124313189215764e+72
7	2.4861480825170347e-112	4.9053706167200877e-110	2.548256466828356e-112
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-1.3603160824255169e+144

Iters

Range

Point

3.9532145147442873e+71

1.0218572913399418e+74

3.3124313189215764e+72

2.4861480825170347e-112

4.9053706167200877e-110

2.548256466828356e-112

-3.0529494422842112e+156

-1.5054982703030158e+138

-1.3603160824255169e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	29
1	49	29
2	49	29

end0.0ms

sample1.2s

Algorithm

intervals

Results

264.0ms	1104×	body	2560	valid
233.0ms	5787×	body	80	valid
170.0ms	898×	body	1280	valid
107.0ms	2923×	body	80	nan
66.0ms	458×	body	640	valid
29.0ms	105×	body	5120	valid
24.0ms	226×	body	320	valid
9.0ms	123×	body	160	valid