Details

sample42.0ms

Algorithm

intervals

Results

15.0ms	236×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	16×	body	320	valid
2.0ms	9×	body	1280	valid
1.0ms	12×	body	160	valid
0.0ms	1×	body	2560	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune4.0ms

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: 25.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.3b	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.4b	(/ (* (- y x) (- z t)) (- a t))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series95.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(* (- y x) (- z t))
50.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
34.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify56.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune158.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 4.6b

Counts

91 → 12

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.6b	(* (- y x) (/ (- z t) (- a t)))
3.3b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

7.0ms	(/ (- z t) (- a t))
16.0ms	(* (- y x) (/ (- z t) (- a t)))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series90.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
31.0ms	(* (- y x) (/ (- z t) (- a t)))
51.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5002	820

prune152.0ms

Filtered

83 candidates to 128 candidates (-54.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	126	14	140

Merged error: 4.6b

Counts

140 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- y x)) (cbrt (- y x)))
0.6b	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t))))
1.1b	(* (cbrt (- y x)) (/ (- z t) (- a t)))
10.4b	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

124×	`cbrt-div`
88×	`frac-times`
73×	`add-sqr-sqrt`
63×	`flip3--` `flip--`
61×	`*-un-lft-identity`
42×	`associate-*l/`
40×	`associate-r`
35×	`cbrt-prod`
32×	`add-exp-log`
29×	`associate-*r/`
27×	`times-frac`
25×	`pow1` `add-cube-cbrt`
18×	`add-cbrt-cube`
17×	`associate-l` `distribute-lft-out--`
16×	`prod-exp` `cbrt-unprod`
15×	`difference-of-squares`
11×	`pow-prod-down`
10×	`swap-sqr`
8×	`unswap-sqr`
6×	`pow1/3` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `*-commutative`
2×	`associate-/r/` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+` `div-inv`

Counts

4 → 207

Calls

4 calls:

10.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
24.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t))))
17.0ms	(* (cbrt (- y x)) (/ (- z t) (- a t)))
3.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t)))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
31.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t))))
85.0ms	(* (cbrt (- y x)) (/ (- z t) (- a t)))
52.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- y x)) (/ (- z t) (- a t)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	951	2877
1	3756	2610
2	5002	2531

prune226.0ms

Filtered

122 candidates to 219 candidates (-79.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	218	15	233

Merged error: 4.6b

Counts

233 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
3.3b	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
3.3b	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
10.4b	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (* (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-div`
6×	`frac-times` `flip3--` `associate-*l/` `flip--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3` `associate-*r/`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 53

Calls

4 calls:

10.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
10.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
10.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
3.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (* (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
92.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
92.0ms	(cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))
51.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (* (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t))))) (cbrt (* (cbrt (- y x)) (/ (- z t) (- a t)))))))

simplify134.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	345	1216
1	997	1079
2	3918	1015
3	5003	979

prune89.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	65	15	80

Merged error: 4.6b

Counts

80 → 15

regimes669.0ms

Accuracy

4.4% (6.9b remaining)

Error of 11.3b against oracle of 4.5b and baseline of 11.7b

bsearch39.0ms

Steps

Iters	Range		Point
8	4.3118155280206625e-21	5.051593265739691e-18	4.379203611830672e-21
4	-2.09799107909261e-137	-1.3475921510364924e-137	-1.3710421175382463e-137

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

334.0ms	7747×	body	80	valid
79.0ms	490×	body	640	valid
54.0ms	274×	body	1280	valid
49.0ms	407×	body	320	valid
22.0ms	272×	body	160	valid
4.0ms	19×	body	2560	valid

Details

sample42.0ms

simplify66.0ms

prune4.0ms

localize9.0ms

rewrite31.0ms

series95.0ms

simplify56.0ms

prune158.0ms

localize12.0ms

rewrite31.0ms

series90.0ms

simplify52.0ms

prune152.0ms

localize13.0ms

rewrite67.0ms

series197.0ms

simplify112.0ms

prune226.0ms

localize18.0ms

rewrite36.0ms

series328.0ms

simplify134.0ms

prune89.0ms

regimes669.0ms

bsearch39.0ms

simplify1.0ms

end0.0ms

sample1.1s

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