Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	180×	body	80	valid
10.0ms	39×	body	2560	valid
8.0ms	35×	body	1280	valid
4.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	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: 33.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b	(- (* b b) (* (* 3.0 a) c))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

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:

21.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg 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)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
80.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
108.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune203.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 5.3b

Counts

83 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.4b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

6.0ms	(- (* b b) (* (* 3.0 a) c))
31.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
23.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
233.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
270.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune365.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	158	12	170

Merged error: 5.3b

Counts

170 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

6.1b	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
9.1b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
23.4b	(cbrt (- (* b b) (* (* 3.0 a) c)))
23.4b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
7.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
4.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series870.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
584.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
97.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	631	1757
1	2984	1588
2	5002	1580

prune360.0ms

Filtered

83 candidates to 77 candidates (92.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	83	12	95

Merged error: 5.3b

Counts

95 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

13.6b	(cbrt (+ 0 (* 3.0 (* a c))))
13.6b	(cbrt (+ 0 (* 3.0 (* a c))))
13.6b	(cbrt (+ 0 (* 3.0 (* a c))))
22.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-prod` `flip-+`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
102.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
101.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	257	530
1	981	490
2	5002	456

prune237.0ms

Filtered

66 candidates to 61 candidates (92.4%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	66	12	78

Merged error: 5.3b

Counts

78 → 12

regimes477.0ms

Accuracy

88.3% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 32.3b

bsearch165.0ms

Steps

Iters	Range	Point
9	1.7907836249739894e-10	2.3719878869137505e-05	2.2452070598618075e-05
9	3.766944934843166e-148	3.4590224569855256e-143	3.3079120607768106e-144
4	-4.3383718458983163e+130	-2.1702536439911652e+130	-4.2691218361104216e+130

Iters

Range

Point

1.7907836249739894e-10

2.3719878869137505e-05

2.2452070598618075e-05

3.766944934843166e-148

3.4590224569855256e-143

3.3079120607768106e-144

-4.3383718458983163e+130

-2.1702536439911652e+130

-4.2691218361104216e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	29
1	48	29
2	48	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

295.0ms	1056×	body	2560	valid
295.0ms	5922×	body	80	valid
191.0ms	872×	body	1280	valid
133.0ms	2904×	body	80	nan
76.0ms	438×	body	640	valid
39.0ms	112×	body	5120	valid
31.0ms	232×	body	320	valid
9.0ms	107×	body	160	valid

Details

sample52.0ms

simplify11.0ms

prune3.0ms

localize13.0ms

rewrite51.0ms

series370.0ms

simplify46.0ms

prune203.0ms

localize15.0ms

rewrite76.0ms

series624.0ms

simplify123.0ms

prune365.0ms

localize20.0ms

rewrite21.0ms

series870.0ms

simplify110.0ms

prune360.0ms

localize20.0ms

rewrite12.0ms

series387.0ms

simplify57.0ms

prune237.0ms

regimes477.0ms

bsearch165.0ms

simplify2.0ms

end0.0ms

sample1.3s

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