Details

sample56.0ms

Algorithm

intervals

Results

10.0ms	193×	body	80	valid
9.0ms	27×	body	2560	valid
7.0ms	29×	body	1280	valid
5.0ms	95×	body	80	nan
4.0ms	19×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	16
1	91	16

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (* b b) (* 4.0 (* a c)))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4959	1319
1	4959	1319

prune160.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 5.2b

Counts

85 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
2.9b	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
9.2b	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
52×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`flip3-+` `flip-+` `div-inv`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod` `associate-/l/`
2×	`flip3--` `frac-2neg` `sub0-neg` `sqrt-div` `prod-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 122

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
8.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
58.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4918	3148
1	4918	3148

prune244.0ms

Filtered

102 candidates to 134 candidates (-31.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	133	10	143

Merged error: 5.2b

Counts

143 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
2.9b	(/ (neg (* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))) (* a 2.0))
9.2b	(* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-exp-log` `add-cbrt-cube`
18×	`times-frac` `associate-l`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
10×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `distribute-lft-out`
3×	`pow-prod-down` `sqrt-prod`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `sqrt-div` `associate-*l/` `associate-/r/` `flip-+` `div-inv`
1×	`+-commutative` `neg-sub0` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `distribute-frac-neg` `associate-r` `clear-num` `associate-/r` `sum-log` `-commutative` `flip--` `associate-/l/` `distribute-neg-frac`

Counts

4 → 95

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(/ (neg (* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))) (* a 2.0))
11.0ms	(* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
34.0ms	(/ (neg (* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))) (* a 2.0))
39.0ms	(* (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a c))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify32.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5004	1912

prune175.0ms

Filtered

82 candidates to 107 candidates (-30.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 5.1b

Counts

117 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) c)
1.6b	(- (* b b) (* 4.0 (* a c)))
2.4b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
69×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
58×	`associate-l`
49×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-/r/`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `div-exp` `associate-r` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `sum-log` `-commutative`

Counts

4 → 119

Calls

4 calls:

17.0ms	(* (/ (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) c)
4.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ (/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) 2.0) c)
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4974	2298
1	4974	2298

prune233.0ms

Filtered

105 candidates to 131 candidates (-24.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Merged error: 5.0b

Counts

139 → 8

regimes292.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.5b

bsearch110.0ms

Steps

Iters	Range	Point
9	9.19707175362887e+95	2.4714310794775493e+104	6.1921107765546395e+103
9	-6.695429941707738e-297	-7.676761036242019e-305	-1.1137175916725923e-303
9	-6.247250655316605e+139	-3.660489123272618e+133	-3.8900654094429814e+133

Iters

Range

Point

9.19707175362887e+95

2.4714310794775493e+104

6.1921107765546395e+103

-6.695429941707738e-297

-7.676761036242019e-305

-1.1137175916725923e-303

-6.247250655316605e+139

-3.660489123272618e+133

-3.8900654094429814e+133

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	65
1	52	65

end0.0ms

sample1.6s

Algorithm

intervals

Results

328.0ms	1069×	body	2560	valid
321.0ms	5818×	body	80	valid
230.0ms	911×	body	1280	valid
149.0ms	2950×	body	80	nan
93.0ms	474×	body	640	valid
41.0ms	111×	body	5120	valid
34.0ms	216×	body	320	valid
11.0ms	116×	body	160	valid

Details

sample56.0ms

simplify3.0ms

prune8.0ms

localize10.0ms

rewrite25.0ms

series64.0ms

simplify47.0ms

prune160.0ms

localize15.0ms

rewrite32.0ms

series129.0ms

simplify67.0ms

prune244.0ms

localize13.0ms

rewrite29.0ms

series102.0ms

simplify32.0ms

prune175.0ms

localize15.0ms

rewrite34.0ms

series71.0ms

simplify52.0ms

prune233.0ms

regimes292.0ms

bsearch110.0ms

simplify1.0ms

end0.0ms

sample1.6s

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