Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.5b	(+ (* (+ x y) z) (* (+ t y) a))
2.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
26.4b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`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×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

10.0ms	(* (+ x y) z)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
39.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
82.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series812.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (+ x y) z)
55.0ms	(+ (* (+ x y) z) (* (+ t y) a))
106.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
628.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	568	1186
1	2526	1087
2	5001	1076

prune446.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.5b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.8b	(- (* (+ t y) a) (* y b))
26.4b	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `flip3--` `pow-flip` `flip3-+` `fma-neg` `diff-log` `prod-diff` `associate-/r/` `flip--` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 167

Calls

4 calls:

22.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
9.0ms	(- (* (+ t y) a) (* y b))
32.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

series881.0ms

Counts

4 → 12

Calls

4 calls:

630.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b)))))
106.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
113.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (- (* (+ t y) a) (* y b))))

simplify78.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	496	2605
1	2228	2401
2	5002	2286

prune411.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
1.8b	(- (* (+ t y) a) (* y b))
26.4b	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `prod-diff` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

3 → 65

Calls

3 calls:

0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
5.0ms	(- (* (+ t y) a) (* y b))
18.0ms	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

series585.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
31.0ms	(- (* (+ t y) a) (* y b))
445.0ms	(/ (fma z (+ x y) (- (* (+ t y) a) (* y b))) (+ (+ x t) y))

simplify114.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	257	781
1	940	719
2	4451	713
3	5001	709

prune271.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
0.9b	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
1.8b	(- (* (+ t y) a) (* y b))
25.4b	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `pow-flip` `frac-2neg` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 103

Calls

4 calls:

0.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
2.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
5.0ms	(- (* (+ t y) a) (* y b))
48.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma z (+ x y) (- (* (+ t y) a) (* y b)))
72.0ms	(/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b))))
33.0ms	(- (* (+ t y) a) (* y b))
112.0ms	(* (+ (+ x t) y) (/ 1 (fma z (+ x y) (- (* (+ t y) a) (* y b)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	386	1147
1	1866	1013
2	5001	981

prune335.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.1b

regimes561.0ms

Accuracy

50.1% (11.2b remaining)

Error of 15.9b against oracle of 4.7b and baseline of 27.2b

bsearch137.0ms

Steps

Iters	Range		Point
8	2.4600082236855723e+39	6.330721831183113e+41	4.5318974852232026e+41
10	-2.740847179348341e+56	-6.345399855322498e+46	-1.827269622806345e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	12
1	40	12
2	40	12

end0.0ms

sample1.0s

Algorithm

intervals

Results

758.0ms	7994×	body	80	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid