Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify97.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	71	10
2	184	10
3	381	10
4	682	10
5	1102	10
6	2122	10
7	4337	10
8	5001	10

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: 26.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
2.5b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`associate-l` `frac-add`
3×	`associate-r` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

6.0ms	(* (+ t y) a)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
17.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series764.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ t y) a)
45.0ms	(+ (* (+ x y) z) (* (+ t y) a))
96.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
598.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify62.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	520	1087
1	2308	1025
2	5001	1025

prune287.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	11	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	11	103

Merged error: 8.3b

Counts

103 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (+ x t) y))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
2.5b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.4b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*l/`
7×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r*`
4×	`div-exp` `frac-add` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (+ (+ x t) y))
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1 (+ (+ x t) y))
46.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
594.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	562	1269
1	2768	1146
2	5002	1104

prune276.0ms

Filtered

130 candidates to 77 candidates (59.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	130	11	141

Merged error: 8.3b

Counts

141 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
2.1b	(+ (* (+ x y) z) (* (+ t y) a))
2.5b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.4b	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

152×	`*-un-lft-identity`
138×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`div-exp` `associate-l/` `associate-/l`
6×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `frac-add`
2×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `associate--l+` `inv-pow`

Counts

4 → 176

Calls

4 calls:

18.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
11.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
16.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

587.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
49.0ms	(+ (* (+ x y) z) (* (+ t y) a))
107.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
97.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify94.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	703	3188
1	3355	2977
2	5002	2859

prune330.0ms

Filtered

188 candidates to 92 candidates (48.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	188	11	199

Merged error: 4.9b

Counts

199 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
2.1b	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
2.5b	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
25.3b	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
12×	`associate-*l/` `distribute-lft-out`
11×	`add-log-exp`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`associate-/r*`
4×	`pow1` `frac-add`
3×	`cbrt-prod` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `pow1/3` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt a)
8.0ms	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
11.0ms	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
16.0ms	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt a)
102.0ms	(+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a)))
162.0ms	(- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b))
681.0ms	(/ (- (+ (* (+ x y) z) (* (* (+ t y) (* (cbrt a) (cbrt a))) (cbrt a))) (* y b)) (+ (+ x t) y))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	518	1551
1	2167	1448
2	5003	1413

prune257.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Merged error: 4.9b

Counts

103 → 11

regimes566.0ms

Accuracy

44.7% (12.1b remaining)

Error of 16.7b against oracle of 4.6b and baseline of 26.5b

bsearch208.0ms

Steps

Iters	Range		Point
8	4.483896561849653e+84	3.73396300242758e+88	5.450037298204365e+86
9	-2.537940135630311e-116	-7.263545656479697e-122	-2.5150150167251363e-116
9	-2.5111433957047454e-55	-1.894298150595098e-61	-1.9251727513763557e-61
8	-2.520549223260671e+50	-1.967744055405134e+47	-5.3523541465978086e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample750.0ms

Algorithm

intervals

Results

485.0ms	7999×	body	80	valid
0.0ms	1×	body	160	valid

Details

sample28.0ms

simplify97.0ms

prune3.0ms

localize14.0ms

rewrite42.0ms

series764.0ms

simplify62.0ms

prune287.0ms

localize16.0ms

rewrite53.0ms

series793.0ms

simplify71.0ms

prune276.0ms

localize16.0ms

rewrite62.0ms

series840.0ms

simplify94.0ms

prune330.0ms

localize19.0ms

rewrite39.0ms

series1.1s

simplify66.0ms

prune257.0ms

regimes566.0ms

bsearch208.0ms

simplify2.0ms

end0.0ms

sample750.0ms

Profiling