Details

sample241.0ms

Algorithm

intervals

Results

210.0ms	278×	body	80	valid
8.0ms	100×	body	80	nan

simplify453.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	141	37
1	141	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 21.9b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5231	1002

prune194.0ms

Filtered

59 candidates to 72 candidates (-22.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Merged error: 5.0b

Counts

73 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
2.7b	(* c (/ a b))
3.3b	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
7×	`pow1`
6×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+` `associate-/l*`

Counts

4 → 82

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(* c (/ a b))
9.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(* c (/ a b))
16.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4973	1077
1	4973	1077

prune201.0ms

Filtered

71 candidates to 94 candidates (-32.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 5.0b

Counts

103 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* c (* (/ (cbrt a) (sqrt b)) (cbrt a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.9b	(/ (* 2.0 c) (+ (* 2.0 (* (* c (* (/ (cbrt a) (sqrt b)) (cbrt a))) (/ (cbrt a) (sqrt b)))) (* b -2)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
15×	`add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `pow-prod-down` `associate-/r*` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `associate-r` `associate-l/` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 71

Calls

4 calls:

9.0ms	(* c (* (/ (cbrt a) (sqrt b)) (cbrt a)))
5.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (* 2.0 c) (+ (* 2.0 (* (* c (* (/ (cbrt a) (sqrt b)) (cbrt a))) (/ (cbrt a) (sqrt b)))) (* b -2)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* c (* (/ (cbrt a) (sqrt b)) (cbrt a)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(/ (* 2.0 c) (+ (* 2.0 (* (* c (* (/ (cbrt a) (sqrt b)) (cbrt a))) (/ (cbrt a) (sqrt b)))) (* b -2)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify29.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5555	1274

prune200.0ms

Filtered

67 candidates to 83 candidates (-23.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 5.0b

Counts

93 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
9.3b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
23.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.8b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`cbrt-prod`
4×	`pow1` `cbrt-div`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `flip3--` `flip3-+` `pow1/3` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `frac-2neg` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

9.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
4.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
31.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
27.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify27.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5034	1463

prune215.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	72	12	84

Merged error: 5.0b

Counts

84 → 12

regimes340.0ms

Accuracy

90.1% (1.6b remaining)

Error of 7.4b against oracle of 5.9b and baseline of 21.7b

bsearch82.0ms

Steps

Iters	Range		Point
11	5.225951737061154e+20	1.968377579606969e+42	8.8878972280964e+41
9	-1.6796181841493287e+154	-2.4052036288306873e+149	-1.8707267733210915e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	95
1	62	95

end0.0ms

sample1.4s

Algorithm

intervals

Results

729.0ms	8761×	body	80	valid
234.0ms	2907×	body	80	nan

Details

sample241.0ms

simplify453.0ms

prune13.0ms

localize36.0ms

rewrite24.0ms

series68.0ms

simplify47.0ms

prune194.0ms

localize25.0ms

rewrite24.0ms

series46.0ms

simplify60.0ms

prune201.0ms

localize30.0ms

rewrite38.0ms

series100.0ms

simplify29.0ms

prune200.0ms

localize30.0ms

rewrite21.0ms

series98.0ms

simplify27.0ms

prune215.0ms

regimes340.0ms

bsearch82.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling